diff --git a/ibis/backends/base/sqlglot/compiler.py b/ibis/backends/base/sqlglot/compiler.py
index 16a8403e4d52..3338d13533dc 100644
--- a/ibis/backends/base/sqlglot/compiler.py
+++ b/ibis/backends/base/sqlglot/compiler.py
@@ -23,6 +23,7 @@
     add_order_by_to_empty_ranking_window_functions,
     empty_in_values_right_side,
     one_to_zero_index,
+    rewrite_capitalize,
     sqlize,
 )
 from ibis.expr.operations.udf import InputType
@@ -179,6 +180,7 @@ class SQLGlotCompiler(abc.ABC):
         one_to_zero_index,
         add_one_to_nth_value_input,
         replace_bucket,
+        rewrite_capitalize,
     )
     """A sequence of rewrites to apply to the expression tree before compilation."""
 
@@ -223,7 +225,6 @@ class SQLGlotCompiler(abc.ABC):
         ops.Asin: "asin",
         ops.Atan2: "atan2",
         ops.Atan: "atan",
-        ops.Capitalize: "initcap",
         ops.Cos: "cos",
         ops.Cot: "cot",
         ops.Count: "count",
diff --git a/ibis/backends/base/sqlglot/rewrites.py b/ibis/backends/base/sqlglot/rewrites.py
index 93cf4db49158..f3cdf7364231 100644
--- a/ibis/backends/base/sqlglot/rewrites.py
+++ b/ibis/backends/base/sqlglot/rewrites.py
@@ -245,6 +245,18 @@ def add_one_to_nth_value_input(_, **kwargs):
     return _.copy(nth=nth)
 
 
+@replace(p.Capitalize)
+def rewrite_capitalize(_, **kwargs):
+    """Rewrite Capitalize in terms of substring, concat, upper, and lower."""
+    first = ops.Uppercase(ops.Substring(_.arg, start=0, length=1))
+    # use length instead of length - 1 to avoid backends complaining about
+    # asking for negative length
+    #
+    # there are at most length - 1 characters, so asking for length is fine
+    rest = ops.Lowercase(ops.Substring(_.arg, start=1, length=ops.StringLength(_.arg)))
+    return ops.StringConcat((first, rest))
+
+
 @replace(p.Sample)
 def rewrite_sample_as_filter(_, **kwargs):
     """Rewrite Sample as `t.filter(random() <= fraction)`.
diff --git a/ibis/backends/bigquery/compiler.py b/ibis/backends/bigquery/compiler.py
index accb2487b2e4..e4cfdfff298c 100644
--- a/ibis/backends/bigquery/compiler.py
+++ b/ibis/backends/bigquery/compiler.py
@@ -225,11 +225,6 @@ def visit_ArrayRepeat(self, op, *, arg, times):
             sg.select(arg[self.f.safe_ordinal(idx)]).from_(self._unnest(series, as_=i))
         )
 
-    def visit_Capitalize(self, op, *, arg):
-        return self.f.concat(
-            self.f.upper(self.f.substr(arg, 1, 1)), self.f.lower(self.f.substr(arg, 2))
-        )
-
     def visit_NthValue(self, op, *, arg, nth):
         if not isinstance(op.nth, ops.Literal):
             raise com.UnsupportedOperationError(
diff --git a/ibis/backends/clickhouse/compiler.py b/ibis/backends/clickhouse/compiler.py
index dbb1a6e1066a..d94fe936763f 100644
--- a/ibis/backends/clickhouse/compiler.py
+++ b/ibis/backends/clickhouse/compiler.py
@@ -452,11 +452,6 @@ def visit_StringSplit(self, op, *, arg, delimiter):
             delimiter, self.cast(arg, dt.String(nullable=False))
         )
 
-    def visit_Capitalize(self, op, *, arg):
-        return self.f.concat(
-            self.f.upper(self.f.substr(arg, 1, 1)), self.f.lower(self.f.substr(arg, 2))
-        )
-
     def visit_GroupConcat(self, op, *, arg, sep, where):
         call = self.agg.groupArray(arg, where=where)
         return self.if_(self.f.empty(call), NULL, self.f.arrayStringConcat(call, sep))
diff --git a/ibis/backends/dask/tests/test_strings.py b/ibis/backends/dask/tests/test_strings.py
index 240d78b2fd17..dfd70e291d3e 100644
--- a/ibis/backends/dask/tests/test_strings.py
+++ b/ibis/backends/dask/tests/test_strings.py
@@ -51,11 +51,6 @@
         param(lambda s: s.reverse(), lambda s: s.str[::-1], id="reverse"),
         param(lambda s: s.lower(), lambda s: s.str.lower(), id="lower"),
         param(lambda s: s.upper(), lambda s: s.str.upper(), id="upper"),
-        param(
-            lambda s: s.capitalize(),
-            lambda s: s.str.capitalize(),
-            id="capitalize",
-        ),
         param(lambda s: s.repeat(2), lambda s: s * 2, id="repeat"),
         param(
             lambda s: s.contains("a"),
diff --git a/ibis/backends/druid/compiler.py b/ibis/backends/druid/compiler.py
index 2be8891c7a15..eb64b6d03fcb 100644
--- a/ibis/backends/druid/compiler.py
+++ b/ibis/backends/druid/compiler.py
@@ -9,7 +9,10 @@
 from ibis.backends.base.sqlglot.compiler import NULL, SQLGlotCompiler
 from ibis.backends.base.sqlglot.datatypes import DruidType
 from ibis.backends.base.sqlglot.dialects import Druid
-from ibis.backends.base.sqlglot.rewrites import rewrite_sample_as_filter
+from ibis.backends.base.sqlglot.rewrites import (
+    rewrite_capitalize,
+    rewrite_sample_as_filter,
+)
 
 
 class DruidCompiler(SQLGlotCompiler):
@@ -17,7 +20,14 @@ class DruidCompiler(SQLGlotCompiler):
 
     dialect = Druid
     type_mapper = DruidType
-    rewrites = (rewrite_sample_as_filter, *SQLGlotCompiler.rewrites)
+    rewrites = (
+        rewrite_sample_as_filter,
+        *(
+            rewrite
+            for rewrite in SQLGlotCompiler.rewrites
+            if rewrite is not rewrite_capitalize
+        ),
+    )
 
     UNSUPPORTED_OPERATIONS = frozenset(
         (
diff --git a/ibis/backends/duckdb/compiler.py b/ibis/backends/duckdb/compiler.py
index 17d599156d16..2f6bbb143823 100644
--- a/ibis/backends/duckdb/compiler.py
+++ b/ibis/backends/duckdb/compiler.py
@@ -317,11 +317,6 @@ def visit_NonNullLiteral(self, op, *, value, dtype):
         else:
             return None
 
-    def visit_Capitalize(self, op, *, arg):
-        return self.f.concat(
-            self.f.upper(self.f.substr(arg, 1, 1)), self.f.lower(self.f.substr(arg, 2))
-        )
-
     def _neg_idx_to_pos(self, array, idx):
         arg_length = self.f.array_size(array)
         return self.if_(
diff --git a/ibis/backends/impala/tests/snapshots/test_string_builtins/test_string_builtins/capitalize/out.sql b/ibis/backends/impala/tests/snapshots/test_string_builtins/test_string_builtins/capitalize/out.sql
index d23a9119ada0..418a92882745 100644
--- a/ibis/backends/impala/tests/snapshots/test_string_builtins/test_string_builtins/capitalize/out.sql
+++ b/ibis/backends/impala/tests/snapshots/test_string_builtins/test_string_builtins/capitalize/out.sql
@@ -1,3 +1,22 @@
 SELECT
-  INITCAP(`t0`.`string_col`) AS `Capitalize(string_col)`
+  CONCAT(
+    UPPER(
+      IF(
+        (
+          0 + 1
+        ) >= 1,
+        SUBSTRING(`t0`.`string_col`, 0 + 1, 1),
+        SUBSTRING(`t0`.`string_col`, 0 + 1 + LENGTH(`t0`.`string_col`), 1)
+      )
+    ),
+    LOWER(
+      IF(
+        (
+          1 + 1
+        ) >= 1,
+        SUBSTRING(`t0`.`string_col`, 1 + 1, LENGTH(`t0`.`string_col`)),
+        SUBSTRING(`t0`.`string_col`, 1 + 1 + LENGTH(`t0`.`string_col`), LENGTH(`t0`.`string_col`))
+      )
+    )
+  ) AS `Capitalize(string_col)`
 FROM `functional_alltypes` AS `t0`
\ No newline at end of file
diff --git a/ibis/backends/impala/tests/test_exprs.py b/ibis/backends/impala/tests/test_exprs.py
index 34aa186bbda7..8fdc4e1b4358 100644
--- a/ibis/backends/impala/tests/test_exprs.py
+++ b/ibis/backends/impala/tests/test_exprs.py
@@ -286,7 +286,6 @@ def test_decimal_builtins_2(con, func, expected):
         (L("   a   ").strip(), "a"),
         (L("   a   ").lstrip(), "a   "),
         (L("   a   ").rstrip(), "   a"),
-        (L("abcd").capitalize(), "Abcd"),
         (L("abcd").substr(0, 2), "ab"),
         (L("abcd").left(2), "ab"),
         (L("abcd").right(2), "cd"),
diff --git a/ibis/backends/mssql/compiler.py b/ibis/backends/mssql/compiler.py
index dd438ae5f867..3e696229a9bf 100644
--- a/ibis/backends/mssql/compiler.py
+++ b/ibis/backends/mssql/compiler.py
@@ -183,13 +183,6 @@ def visit_StringLength(self, op, *, arg):
         """
         return paren(self.f.len(self.f.concat("A", arg, "Z")) - 2)
 
-    def visit_Capitalize(self, op, *, arg):
-        length = paren(self.f.len(self.f.concat("A", arg, "Z")) - 2)
-        return self.f.concat(
-            self.f.upper(self.f.substring(arg, 1, 1)),
-            self.f.lower(self.f.substring(arg, 2, length - 1)),
-        )
-
     def visit_GroupConcat(self, op, *, arg, sep, where):
         if where is not None:
             arg = self.if_(where, arg, NULL)
diff --git a/ibis/backends/mysql/compiler.py b/ibis/backends/mysql/compiler.py
index c0e720b3e33c..41460616badd 100644
--- a/ibis/backends/mysql/compiler.py
+++ b/ibis/backends/mysql/compiler.py
@@ -291,11 +291,6 @@ def visit_StringFind(self, op, *, arg, substr, start, end):
             return self.f.locate(substr, arg, start + 1)
         return self.f.locate(substr, arg)
 
-    def visit_Capitalize(self, op, *, arg):
-        return self.f.concat(
-            self.f.upper(self.f.left(arg, 1)), self.f.lower(self.f.substr(arg, 2))
-        )
-
     def visit_LRStrip(self, op, *, arg, position):
         return reduce(
             lambda arg, char: self.f.trim(this=arg, position=position, expression=char),
diff --git a/ibis/backends/pandas/tests/test_strings.py b/ibis/backends/pandas/tests/test_strings.py
index e583cb53437e..3aa9b4bc5a00 100644
--- a/ibis/backends/pandas/tests/test_strings.py
+++ b/ibis/backends/pandas/tests/test_strings.py
@@ -49,11 +49,6 @@
         param(lambda s: s.reverse(), lambda s: s.str[::-1], id="reverse"),
         param(lambda s: s.lower(), lambda s: s.str.lower(), id="lower"),
         param(lambda s: s.upper(), lambda s: s.str.upper(), id="upper"),
-        param(
-            lambda s: s.capitalize(),
-            lambda s: s.str.capitalize(),
-            id="capitalize",
-        ),
         param(lambda s: s.repeat(2), lambda s: s * 2, id="repeat"),
         param(
             lambda s: s.contains("a"),
diff --git a/ibis/backends/polars/compiler.py b/ibis/backends/polars/compiler.py
index f51ca271dd55..22a88d84cb58 100644
--- a/ibis/backends/polars/compiler.py
+++ b/ibis/backends/polars/compiler.py
@@ -503,7 +503,6 @@ def in_values(op, **kw):
     ops.RStrip: "strip_chars_end",
     ops.Lowercase: "to_lowercase",
     ops.Uppercase: "to_uppercase",
-    ops.Capitalize: "to_titlecase",
 }
 
 
@@ -514,6 +513,15 @@ def string_length(op, **kw):
     return arg.str.len_bytes().cast(typ)
 
 
+@translate.register(ops.Capitalize)
+def capitalize(op, **kw):
+    arg = translate(op.arg, **kw)
+    typ = dtype_to_polars(op.dtype)
+    first = arg.str.slice(0, 1).str.to_uppercase()
+    rest = arg.str.slice(1, None).str.to_lowercase()
+    return (first + rest).cast(typ)
+
+
 @translate.register(ops.StringUnary)
 def string_unary(op, **kw):
     arg = translate(op.arg, **kw)
diff --git a/ibis/backends/postgres/tests/test_functions.py b/ibis/backends/postgres/tests/test_functions.py
index 64e3f3cfc25a..de1256853df3 100644
--- a/ibis/backends/postgres/tests/test_functions.py
+++ b/ibis/backends/postgres/tests/test_functions.py
@@ -243,14 +243,6 @@ def test_string_contains(con, haystack, needle, expected):
     assert con.execute(expr) == expected
 
 
-@pytest.mark.parametrize(
-    ("value", "expected"),
-    [("foo bar foo", "Foo Bar Foo"), ("foobar Foo", "Foobar Foo")],
-)
-def test_capitalize(con, value, expected):
-    assert con.execute(L(value).capitalize()) == expected
-
-
 def test_repeat(con):
     expr = L("bar ").repeat(3)
     assert con.execute(expr) == "bar bar bar "
diff --git a/ibis/backends/risingwave/tests/test_functions.py b/ibis/backends/risingwave/tests/test_functions.py
index d680fb3190f9..04281a722d9c 100644
--- a/ibis/backends/risingwave/tests/test_functions.py
+++ b/ibis/backends/risingwave/tests/test_functions.py
@@ -90,14 +90,6 @@ def test_string_contains(con, haystack, needle, expected):
     assert con.execute(expr) == expected
 
 
-@pytest.mark.parametrize(
-    ("value", "expected"),
-    [("foo bar foo", "Foo Bar Foo"), ("foobar Foo", "Foobar Foo")],
-)
-def test_capitalize(con, value, expected):
-    assert con.execute(L(value).capitalize()) == expected
-
-
 def test_repeat(con):
     expr = L("bar ").repeat(3)
     assert con.execute(expr) == "bar bar bar "
diff --git a/ibis/backends/sqlite/udf.py b/ibis/backends/sqlite/udf.py
index 380be055095e..d4d646dbb95f 100644
--- a/ibis/backends/sqlite/udf.py
+++ b/ibis/backends/sqlite/udf.py
@@ -235,11 +235,6 @@ def _ibis_string_ascii(string):
     return ord(string[0])
 
 
-@udf
-def _ibis_capitalize(string):
-    return string.capitalize()
-
-
 @udf
 def _ibis_rpad(string, width, pad):
     return string.ljust(width, pad)[:width]
diff --git a/ibis/backends/tests/test_string.py b/ibis/backends/tests/test_string.py
index 30151b01b668..2595492e0803 100644
--- a/ibis/backends/tests/test_string.py
+++ b/ibis/backends/tests/test_string.py
@@ -562,11 +562,6 @@ def uses_java_re(t):
             lambda t: t.string_col.str.rstrip(),
             id="rstrip",
         ),
-        param(
-            lambda t: t.string_col.capitalize(),
-            lambda t: t.string_col.str.capitalize(),
-            id="capitalize",
-        ),
         param(
             lambda t: t.date_string_col.substr(2, 3),
             lambda t: t.date_string_col.str[2:5],
@@ -844,11 +839,52 @@ def test_parse_url(con, result_func, expected):
     assert result == expected
 
 
-def test_capitalize(con):
-    s = ibis.literal("aBc")
-    expected = "Abc"
+@pytest.mark.parametrize(
+    ("inp, expected"),
+    [
+        param(
+            None,
+            None,
+            id="none",
+            marks=[
+                pytest.mark.notyet(
+                    ["druid"],
+                    raises=PyDruidProgrammingError,
+                    reason="illegal use of NULL",
+                )
+            ],
+        ),
+        param(
+            "",
+            "",
+            id="empty",
+            marks=[
+                pytest.mark.notyet(
+                    ["oracle"],
+                    reason="https://github.com/oracle/python-oracledb/issues/298",
+                    raises=AssertionError,
+                ),
+                pytest.mark.notyet(["exasol"], raises=AssertionError),
+            ],
+        ),
+        param("Abc", "Abc", id="no_change"),
+        param("abc", "Abc", id="lower_to_upper"),
+        param("aBC", "Abc", id="mixed_to_upper"),
+        param(" abc", " abc", id="leading_space"),
+        param("9abc", "9abc", id="leading_digit"),
+        param("aBc dEf", "Abc def", id="mixed_with_space"),
+        param("aBc-dEf", "Abc-def", id="mixed_with_hyphen"),
+        param("aBc1dEf", "Abc1def", id="mixed_with_digit"),
+    ],
+)
+def test_capitalize(con, inp, expected):
+    s = ibis.literal(inp, type="string")
     expr = s.capitalize()
-    assert con.execute(expr) == expected
+    result = con.execute(expr)
+    if expected is not None:
+        assert result == expected
+    else:
+        assert pd.isnull(result)
 
 
 @pytest.mark.notimpl(
diff --git a/ibis/expr/types/strings.py b/ibis/expr/types/strings.py
index 10d3d6331e77..8a3a6a4c5903 100644
--- a/ibis/expr/types/strings.py
+++ b/ibis/expr/types/strings.py
@@ -388,7 +388,10 @@ def rstrip(self) -> StringValue:
         return ops.RStrip(self).to_expr()
 
     def capitalize(self) -> StringValue:
-        """Capitalize the input string.
+        """Uppercase the first letter, lowercase the rest.
+
+        This API matches the semantics of the Python [](`str.capitalize`)
+        method.
 
         Returns
         -------
@@ -399,7 +402,7 @@ def capitalize(self) -> StringValue:
         --------
         >>> import ibis
         >>> ibis.options.interactive = True
-        >>> t = ibis.memtable({"s": ["abc", "def", "ghi"]})
+        >>> t = ibis.memtable({"s": ["aBC", " abc", "ab cd", None]})
         >>> t.s.capitalize()
         ┏━━━━━━━━━━━━━━━┓
         ┃ Capitalize(s) ┃
@@ -407,14 +410,22 @@ def capitalize(self) -> StringValue:
         │ string        │
         ├───────────────┤
         │ Abc           │
-        │ Def           │
-        │ Ghi           │
+        │  abc          │
+        │ Ab cd         │
+        │ NULL          │
         └───────────────┘
         """
         return ops.Capitalize(self).to_expr()
 
     initcap = capitalize
 
+    @util.deprecated(
+        instead="use the `capitalize` method", as_of="9.0", removed_in="10.0"
+    )
+    def initcap(self) -> StringValue:
+        """Deprecated. Use `capitalize` instead."""
+        return self.capitalize()
+
     def __contains__(self, *_: Any) -> bool:
         raise TypeError("Use string_expr.contains(arg)")