@@ -18,6 +18,7 @@ use crate::dtype::FieldNames;
 use crate::dtype::Nullability;
 use crate::expr::BoundExpression;
 use crate::expr::Expression;
+use crate::expr::Lambda;
 use crate::scalar::Scalar;
 use crate::scalar::ScalarValue;
 use crate::scalar_fn::EmptyOptions;
@@ -45,6 +46,8 @@ use crate::scalar_fn::fns::list_contains::ListContains;
 use crate::scalar_fn::fns::list_contains::ListContainsOptions;
 use crate::scalar_fn::fns::list_length::ListLength;
 use crate::scalar_fn::fns::list_sum::ListSum;
+use crate::scalar_fn::fns::list_transform::ListTransform;
+use crate::scalar_fn::fns::list_transform::ListTransformOptions;
 use crate::scalar_fn::fns::literal::Literal;
 use crate::scalar_fn::fns::mask::Mask;
 use crate::scalar_fn::fns::merge::DuplicateHandling;
@@ -153,8 +156,7 @@ pub fn bound_get_item(field: impl Into<FieldName>, child: BoundExpression) -> Bo
 
 /// Creates an expression that reads the parameter `name` of the enclosing lambda.
 ///
-/// It is only meaningful in the body of a [`Lambda`](crate::expr::Lambda). Anywhere else it fails
-/// to bind.
+/// It is only meaningful in the body of a [`Lambda`]. Anywhere else it fails to bind.
 ///
 /// ```rust
 /// # use vortex_array::dtype::{DType, Nullability, PType};
@@ -1391,6 +1393,22 @@ pub fn bound_list_sum_opts(
         .vortex_expect("list-sum expressions require a numeric list child")
 }
 
+// ---- ListTransform ----
+
+/// Creates an expression that applies a lambda to every element of each list.
+///
+/// The lambda takes one parameter, the element.
+///
+/// ```rust
+/// # use vortex_array::expr::{Lambda, checked_add, col, list_transform, lit, var};
+/// let lambda = Lambda::new(["x"], checked_add(var("x"), lit(1_i32))).unwrap();
+/// let expr = list_transform(col("l"), lambda);
+/// assert_eq!(expr.to_string(), "vortex.list.transform($.l, (x) -> (@x + 1i32))");
+/// ```
+pub fn list_transform(list: Expression, lambda: Lambda) -> Expression {
+    ListTransform.new_expr(ListTransformOptions::Lambda(lambda), [list])
+}
+
 /// Reinterpret timestamp wall times in `options.time_zone`, preserving the time unit.
 ///
 /// `ambiguous` is a UTF-8 expression containing `raise`, `earliest`, `latest`, or `null`.
 
@@ -88,6 +88,7 @@ pub use exprs::list_contains_opts;
 pub use exprs::list_length;
 pub use exprs::list_sum;
 pub use exprs::list_sum_opts;
+pub use exprs::list_transform;
 pub use exprs::lit;
 pub use exprs::lt;
 pub use exprs::lt_eq;
 
@@ -0,0 +1,236 @@
+// SPDX-License-Identifier: Apache-2.0
+// SPDX-FileCopyrightText: Copyright the Vortex contributors
+
+#[cfg(test)]
+mod tests;
+
+use std::fmt;
+use std::fmt::Display;
+use std::fmt::Formatter;
+use std::sync::Arc;
+
+use itertools::Itertools;
+use vortex_error::VortexResult;
+use vortex_error::vortex_bail;
+use vortex_error::vortex_ensure;
+use vortex_error::vortex_ensure_eq;
+use vortex_session::registry::CachedId;
+
+use crate::ArrayRef;
+use crate::ExecutionCtx;
+use crate::IntoArray;
+use crate::arrays::List;
+use crate::arrays::ListArray;
+use crate::arrays::ListViewArray;
+use crate::arrays::list::ListArrayExt;
+use crate::arrays::list::ListArraySlotsExt;
+use crate::arrays::listview::ListViewArrayExt;
+use crate::arrays::listview::ListViewArraySlotsExt;
+use crate::arrays::listview::ListViewRebuildMode;
+use crate::dtype::DType;
+use crate::dtype::FieldName;
+use crate::expr::BoundLambda;
+use crate::expr::Lambda;
+use crate::expr::display::ExprDisplay;
+use crate::scalar_fn::Arity;
+use crate::scalar_fn::ChildName;
+use crate::scalar_fn::ExecutionArgs;
+use crate::scalar_fn::ScalarFnId;
+use crate::scalar_fn::ScalarFnVTable;
+
+/// Apply a lambda to every element of each list, keeping each list's length and validity.
+///
+/// The lambda takes one parameter, the element. The only child is the list, of `List` dtype in any
+/// encoding, and the result is a `List` of the same shape. A lambda that can fail runs only on the
+/// elements of valid lists.
+#[derive(Clone)]
+pub struct ListTransform;
+
+/// The lambda of a [`ListTransform`], as written or bound to the element's dtype.
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub enum ListTransformOptions {
+    /// The lambda as written, in an [`Expression`](crate::expr::Expression).
+    Lambda(Lambda),
+    /// The lambda bound to the element's dtype, in a
+    /// [`BoundExpression`](crate::expr::BoundExpression) or an array.
+    Bound(BoundLambda),
+}
+
+impl Display for ListTransformOptions {
+    fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::Lambda(lambda) => lambda.fmt(f),
+            Self::Bound(lambda) => lambda.fmt(f),
+        }
+    }
+}
+
+impl ScalarFnVTable for ListTransform {
+    type Options = ListTransformOptions;
+
+    fn id(&self) -> ScalarFnId {
+        static ID: CachedId = CachedId::new("vortex.list.transform");
+        *ID
+    }
+
+    fn arity(&self, _options: &ListTransformOptions) -> Arity {
+        Arity::Exact(1)
+    }
+
+    fn child_name(&self, _options: &ListTransformOptions, child_idx: usize) -> ChildName {
+        match child_idx {
+            0 => ChildName::from("list"),
+            _ => unreachable!("Invalid child index {child_idx} for list_transform()"),
+        }
+    }
+
+    fn fmt_sql(
+        &self,
+        options: &ListTransformOptions,
+        expr: &dyn ExprDisplay,
+        f: &mut Formatter<'_>,
+    ) -> fmt::Result {
+        write!(f, "{}({}, {options})", self.id(), expr.display_child(0))
+    }
+
+    fn return_dtype(&self, options: &ListTransformOptions, args: &[DType]) -> VortexResult<DType> {
+        let element = match options {
+            ListTransformOptions::Lambda(lambda) => {
+                lambda.return_dtype(&element_dtype(&args[0], lambda.params())?)?
+            }
+            ListTransformOptions::Bound(lambda) => {
+                check_bound_to(lambda, &args[0])?;
+                lambda.dtype().clone()
+            }
+        };
+        Ok(DType::List(Arc::new(element), args[0].nullability()))
+    }
+
+    fn bind_options(
+        &self,
+        options: &ListTransformOptions,
+        args: &[DType],
+    ) -> VortexResult<Option<ListTransformOptions>> {
+        match options {
+            ListTransformOptions::Lambda(lambda) => {
+                let element = element_dtype(&args[0], lambda.params())?;
+                Ok(Some(ListTransformOptions::Bound(lambda.bind(&element)?)))
+            }
+            ListTransformOptions::Bound(lambda) => {
+                check_bound_to(lambda, &args[0])?;
+                Ok(None)
+            }
+        }
+    }
+
+    fn execute(
+        &self,
+        options: &ListTransformOptions,
+        args: &dyn ExecutionArgs,
+        ctx: &mut ExecutionCtx,
+    ) -> VortexResult<ArrayRef> {
+        let ListTransformOptions::Bound(lambda) = options else {
+            vortex_bail!("list_transform()'s lambda is not bound");
+        };
+        match args.get(0)?.try_downcast::<List>() {
+            Ok(list) => transform_list(list, lambda, ctx),
+            Err(list) => transform_list_view(list.execute::<ListViewArray>(ctx)?, lambda, ctx),
+        }
+    }
+
+    fn is_strict(&self, _options: &ListTransformOptions) -> bool {
+        true
+    }
+
+    fn is_infallible(&self, options: &ListTransformOptions) -> bool {
+        match options {
+            ListTransformOptions::Lambda(lambda) => lambda.is_infallible(),
+            ListTransformOptions::Bound(lambda) => lambda.is_infallible(),
+        }
+    }
+}
+
+/// Check that a bound lambda's parameter has the element dtype of a list of this dtype.
+fn check_bound_to(lambda: &BoundLambda, list: &DType) -> VortexResult<()> {
+    let element = element_dtype(list, lambda.params().names().as_ref())?;
+    vortex_ensure!(
+        lambda.is_bound_to(&element),
+        "list_transform()'s lambda {lambda} is bound to element dtype {}, not {}",
+        lambda.params().fields().format(", "),
+        element[0]
+    );
+    Ok(())
+}
+
+/// The dtype of the lambda's one parameter, the element, for a list of this dtype.
+fn element_dtype(list: &DType, params: &[FieldName]) -> VortexResult<[DType; 1]> {
+    let DType::List(element, _) = list else {
+        vortex_bail!("list_transform() takes a List, got {list}");
+    };
+    vortex_ensure!(
+        params.len() == 1,
+        "list_transform() takes a lambda of one parameter, the element, not ({})",
+        params.iter().format(", ")
+    );
+    Ok([element.as_ref().clone()])
+}
+
+/// The lambda over a list's elements, inside the list's offsets and validity.
+///
+/// A lambda that can fail runs only on the elements valid lists reference. One that can't runs on
+/// every element from the first list to the last: results under null lists are never read.
+fn transform_list(
+    list: ListArray,
+    lambda: &BoundLambda,
+    ctx: &mut ExecutionCtx,
+) -> VortexResult<ArrayRef> {
+    let list = if lambda.is_infallible() {
+        trim_ends(list, ctx)?
+    } else {
+        list.compact(ctx)?
+    };
+    let values = lambda.evaluate(vec![list.elements().clone()], list.elements().len())?;
+    vortex_ensure_eq!(values.len(), list.elements().len());
+    // SAFETY: the offsets and validity are the list's, over one value per element.
+    Ok(
+        unsafe { ListArray::new_unchecked(values, list.offsets().clone(), list.list_validity()) }
+            .into_array(),
+    )
+}
+
+/// The lambda over a list view's elements, inside the view's offsets, sizes and validity.
+///
+/// A lambda that can fail runs only on the elements valid lists reference.
+fn transform_list_view(
+    view: ListViewArray,
+    lambda: &BoundLambda,
+    ctx: &mut ExecutionCtx,
+) -> VortexResult<ArrayRef> {
+    let view = if lambda.is_infallible() {
+        view
+    } else {
+        view.rebuild(ListViewRebuildMode::MakeExactWithEmptyNulls, ctx)?
+    };
+    let values = lambda.evaluate(vec![view.elements().clone()], view.elements().len())?;
+    vortex_ensure_eq!(values.len(), view.elements().len());
+    // SAFETY: the offsets, sizes and validity are the view's, over one value per element, so the
+    // views keep their bounds and their layout.
+    Ok(unsafe {
+        ListViewArray::new_unchecked(
+            values,
+            view.offsets().clone(),
+            view.sizes().clone(),
+            view.listview_validity(),
+        )
+        .with_zero_copy_to_list(view.is_zero_copy_to_list())
+    }
+    .into_array())
+}
+
+/// The list without what comes before its first list and after its last.
+fn trim_ends(list: ListArray, ctx: &mut ExecutionCtx) -> VortexResult<ListArray> {
+    if list.offset_at(0, ctx)? == 0 && list.offset_at(list.len(), ctx)? == list.elements().len() {
+        return Ok(list);
+    }
+    list.reset_offsets(false, ctx)
+}