diff --git a/datafusion/optimizer/src/push_down_filter.rs b/datafusion/optimizer/src/push_down_filter.rs
index 8c2eb96a48d8..ae986b3c84dd 100644
--- a/datafusion/optimizer/src/push_down_filter.rs
+++ b/datafusion/optimizer/src/push_down_filter.rs
@@ -12,7 +12,8 @@
 // specific language governing permissions and limitations
 // under the License.
 
-//! Push Down Filter optimizer rule ensures that filters are applied as early as possible in the plan
+//! [`PushDownFilter`] Moves filters so they are applied as early as possible in
+//! the plan.
 
 use crate::optimizer::ApplyOrder;
 use crate::utils::{conjunction, split_conjunction, split_conjunction_owned};
@@ -33,31 +34,93 @@ use itertools::Itertools;
 use std::collections::{HashMap, HashSet};
 use std::sync::Arc;
 
-/// Push Down Filter optimizer rule pushes filter clauses down the plan
+/// Optimizer rule for pushing (moving) filter expressions down in a plan so
+/// they are applied as early as possible.
+///
 /// # Introduction
-/// A filter-commutative operation is an operation whose result of filter(op(data)) = op(filter(data)).
-/// An example of a filter-commutative operation is a projection; a counter-example is `limit`.
 ///
-/// The filter-commutative property is column-specific. An aggregate grouped by A on SUM(B)
-/// can commute with a filter that depends on A only, but does not commute with a filter that depends
-/// on SUM(B).
+/// The goal of this rule is to improve query performance by eliminating
+/// redundant work.
+///
+/// For example, given a plan that sorts all values where `a > 10`:
+///
+/// ```text
+///  Filter (a > 10)
+///    Sort (a, b)
+/// ```
+///
+/// A better plan is to  filter the data *before* the Sort, which sorts fewer
+/// rows and therefore does less work overall:
+///
+/// ```text
+///  Sort (a, b)
+///    Filter (a > 10)  <-- Filter is moved before the sort
+/// ```
+///
+/// However it is not always possible to push filters down. For example, given a
+/// plan that finds the top 3 values and then keeps only those that are greater
+/// than 10, if the filter is pushed below the limit it would produce a
+/// different result.
+///
+/// ```text
+///  Filter (a > 10)   <-- can not move this Filter before the limit
+///    Limit (fetch=3)
+///      Sort (a, b)
+/// ```
+///
+///
+/// More formally, a filter-commutative operation is an operation `op` that
+/// satisfies `filter(op(data)) = op(filter(data))`.
+///
+/// The filter-commutative property is plan and column-specific. A filter on `a`
+/// can be pushed through a `Aggregate(group_by = [a], agg=[SUM(b))`. However, a
+/// filter on  `SUM(b)` can not be pushed through the same aggregate.
+///
+/// # Handling Conjunctions
+///
+/// It is possible to only push down **part** of a filter expression if is
+/// connected with `AND`s (more formally if it is a "conjunction").
+///
+/// For example, given the following plan:
+///
+/// ```text
+/// Filter(a > 10 AND SUM(b) < 5)
+///   Aggregate(group_by = [a], agg = [SUM(b))
+/// ```
+///
+/// The `a > 10` is commutative with the `Aggregate` but  `SUM(b) < 5` is not.
+/// Therefore it is possible to only push part of the expression, resulting in:
+///
+/// ```text
+/// Filter(SUM(b) < 5)
+///   Aggregate(group_by = [a], agg = [SUM(b))
+///     Filter(a > 10)
+/// ```
+///
+/// # Handling Column Aliases
 ///
-/// This optimizer commutes filters with filter-commutative operations to push the filters
-/// the closest possible to the scans, re-writing the filter expressions by every
-/// projection that changes the filter's expression.
+/// This optimizer must sometimes handle re-writing filter expressions when they
+/// pushed, for example if there is a projection that aliases `a+1` to `"b"`:
 ///
-/// Filter: b Gt Int64(10)
-///     Projection: a AS b
+/// ```text
+/// Filter (b > 10)
+///     Projection: [a+1 AS "b"]  <-- changes the name of `a+1` to `b`
+/// ```
 ///
-/// is optimized to
+/// To apply the filter prior to the `Projection`, all references to `b` must be
+/// rewritten to `a+1`:
 ///
-/// Projection: a AS b
-///     Filter: a Gt Int64(10)  <--- changed from b to a
+/// ```text
+/// Projection: a AS "b"
+///     Filter: (a + 1 > 10)  <--- changed from b to a + 1
+/// ```
+/// # Implementation Notes
 ///
-/// This performs a single pass through the plan. When it passes through a filter, it stores that filter,
-/// and when it reaches a node that does not commute with it, it adds the filter to that place.
-/// When it passes through a projection, it re-writes the filter's expression taking into account that projection.
-/// When multiple filters would have been written, it `AND` their expressions into a single expression.
+/// This implementation performs a single pass through the plan, "pushing" down
+/// filters. When it passes through a filter, it stores that filter, and when it
+/// reaches a plan node that does not commute with that filter, it adds the
+/// filter to that place. When it passes through a projection, it re-writes the
+/// filter's expression taking into account that projection.
 #[derive(Default)]
 pub struct PushDownFilter {}