diff --git a/geo-types/CHANGES.md b/geo-types/CHANGES.md
index 064eb9f737..84e192f59e 100644
--- a/geo-types/CHANGES.md
+++ b/geo-types/CHANGES.md
@@ -2,10 +2,12 @@
 
 ## Unreleased
 
+* BREAKING: Make `Rect::to_lines` return lines in winding order for `Rect::to_polygon`.
+  * <https://github.com/georust/geo/pull/757>
 * Note: All crates have been migrated to Rust 2021 edition. The MSRV when installing the latest dependencies has increased to 1.56.
   * <https://github.com/georust/geo/pull/741>
 * Macros `coord!`, `point!`, `line_string!`, and `polygon!` now support trailing commas such as `coord! { x: 181.2, y: 51.79, }`
-  * <https://github.com/georust/geo/pull/752> 
+  * <https://github.com/georust/geo/pull/752>
 
 ## 0.7.3
 
diff --git a/geo-types/src/rect.rs b/geo-types/src/rect.rs
index 6101c1f564..568c1d9ddf 100644
--- a/geo-types/src/rect.rs
+++ b/geo-types/src/rect.rs
@@ -248,8 +248,8 @@ impl<T: CoordNum> Rect<T> {
             ),
             Line::new(
                 coord! {
-                    x: self.min.x,
-                    y: self.min.y,
+                    x: self.max.x,
+                    y: self.max.y,
                 },
                 coord! {
                     x: self.max.x,
@@ -262,8 +262,8 @@ impl<T: CoordNum> Rect<T> {
                     y: self.min.y,
                 },
                 coord! {
-                    x: self.max.x,
-                    y: self.max.y,
+                    x: self.min.x,
+                    y: self.min.y,
                 },
             ),
         ]
diff --git a/geo/CHANGES.md b/geo/CHANGES.md
index cbcf541388..aeb173c494 100644
--- a/geo/CHANGES.md
+++ b/geo/CHANGES.md
@@ -2,6 +2,9 @@
 
 ## Unreleased
 
+* Add `LinesIter` algorithm to iterate over the lines in geometries.
+  * Very similar to `CoordsIter`, but only implemented where it makes sense (e.g., for `Polygon`, `Rect`, but not `Point`).
+  * <https://github.com/georust/geo/pull/757>
 * Add `Default` constraint to all `CoordNum`/`CoordFloat` values.
 
 ## 0.19.0
diff --git a/geo/src/algorithm/lines_iter.rs b/geo/src/algorithm/lines_iter.rs
new file mode 100644
index 0000000000..8f3d2374fa
--- /dev/null
+++ b/geo/src/algorithm/lines_iter.rs
@@ -0,0 +1,303 @@
+use crate::{
+    CoordNum, Coordinate, Line, LineString, MultiLineString, MultiPolygon, Polygon, Rect, Triangle,
+};
+use core::slice;
+use std::fmt::Debug;
+use std::iter;
+
+/// Iterate over lines of a geometry.
+pub trait LinesIter<'a> {
+    type Scalar: CoordNum;
+    type Iter: Iterator<Item = Line<Self::Scalar>>;
+
+    /// Iterate over all exterior and (if any) interior lines of a geometry.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use geo::line_string;
+    /// use geo::lines_iter::LinesIter;
+    /// use geo::{Coordinate, Line};
+    ///
+    /// let ls = line_string![
+    ///     (x: 1., y: 2.),
+    ///     (x: 23., y: 82.),
+    ///     (x: -1., y: 0.),
+    /// ];
+    ///
+    /// let mut iter = ls.lines_iter();
+    /// assert_eq!(
+    ///     Some(Line::new(
+    ///         Coordinate { x: 1., y: 2. },
+    ///         Coordinate { x: 23., y: 82. }
+    ///     )),
+    ///     iter.next()
+    /// );
+    /// assert_eq!(
+    ///     Some(Line::new(
+    ///         Coordinate { x: 23., y: 82. },
+    ///         Coordinate { x: -1., y: 0. }
+    ///     )),
+    ///     iter.next()
+    /// );
+    /// assert_eq!(None, iter.next());
+    /// ```
+    fn lines_iter(&'a self) -> Self::Iter;
+}
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for Line<T> {
+    type Scalar = T;
+    type Iter = iter::Copied<iter::Once<&'a Line<Self::Scalar>>>;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        iter::once(self).copied()
+    }
+}
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for LineString<T> {
+    type Scalar = T;
+    type Iter = LineStringIter<'a, Self::Scalar>;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        LineStringIter::new(self)
+    }
+}
+
+/// Iterator over lines in a [LineString].
+#[derive(Debug)]
+pub struct LineStringIter<'a, T: CoordNum>(slice::Windows<'a, Coordinate<T>>);
+
+impl<'a, T: CoordNum> LineStringIter<'a, T> {
+    fn new(line_string: &'a LineString<T>) -> Self {
+        Self(line_string.0.windows(2))
+    }
+}
+
+impl<'a, T: CoordNum> Iterator for LineStringIter<'a, T> {
+    type Item = Line<T>;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        // Can't use LineString::lines() because it returns an `impl Trait`
+        // and there is no way to name that type in `LinesIter::Iter` until [RFC 2071] is stabilized.
+        //
+        // [RFC 2071]: https://rust-lang.github.io/rfcs/2071-impl-trait-existential-types.html
+        self.0.next().map(|w| {
+            // SAFETY: slice::windows(2) is guaranteed to yield a slice with exactly 2 elements
+            unsafe { Line::new(*w.get_unchecked(0), *w.get_unchecked(1)) }
+        })
+    }
+}
+
+type MultiLineStringIter<'a, T> =
+    iter::Flatten<MapLinesIter<'a, slice::Iter<'a, LineString<T>>, LineString<T>>>;
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for MultiLineString<T> {
+    type Scalar = T;
+    type Iter = MultiLineStringIter<'a, Self::Scalar>;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        MapLinesIter(self.0.iter()).flatten()
+    }
+}
+
+type PolygonIter<'a, T> = iter::Chain<
+    LineStringIter<'a, T>,
+    iter::Flatten<MapLinesIter<'a, slice::Iter<'a, LineString<T>>, LineString<T>>>,
+>;
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for Polygon<T> {
+    type Scalar = T;
+    type Iter = PolygonIter<'a, Self::Scalar>;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        self.exterior()
+            .lines_iter()
+            .chain(MapLinesIter(self.interiors().iter()).flatten())
+    }
+}
+
+type MultiPolygonIter<'a, T> =
+    iter::Flatten<MapLinesIter<'a, slice::Iter<'a, Polygon<T>>, Polygon<T>>>;
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for MultiPolygon<T> {
+    type Scalar = T;
+    type Iter = MultiPolygonIter<'a, Self::Scalar>;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        MapLinesIter(self.0.iter()).flatten()
+    }
+}
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for Rect<T> {
+    type Scalar = T;
+    type Iter = <[Line<Self::Scalar>; 4] as IntoIterator>::IntoIter;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        self.to_lines().into_iter()
+    }
+}
+
+impl<'a, T: CoordNum + 'a> LinesIter<'a> for Triangle<T> {
+    type Scalar = T;
+    type Iter = <[Line<Self::Scalar>; 3] as IntoIterator>::IntoIter;
+
+    fn lines_iter(&'a self) -> Self::Iter {
+        self.to_lines().into_iter()
+    }
+}
+
+/// Utility to transform Iterator<LinesIter> into Iterator<Iterator<Line>>.
+#[derive(Debug)]
+pub struct MapLinesIter<'a, Iter1: Iterator<Item = &'a Iter2>, Iter2: 'a + LinesIter<'a>>(Iter1);
+
+impl<'a, Iter1: Iterator<Item = &'a Iter2>, Iter2: LinesIter<'a>> Iterator
+    for MapLinesIter<'a, Iter1, Iter2>
+{
+    type Item = Iter2::Iter;
+
+    fn next(&mut self) -> Option<Self::Item> {
+        self.0.next().map(|g| g.lines_iter())
+    }
+}
+
+#[cfg(test)]
+mod test {
+
+    use super::LinesIter;
+    use crate::{
+        line_string, polygon, Coordinate, Line, LineString, MultiLineString, MultiPolygon, Rect,
+        Triangle,
+    };
+
+    #[test]
+    fn test_line() {
+        let line = Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 5., y: 10. });
+        let want = vec![Line::new(
+            Coordinate { x: 0., y: 0. },
+            Coordinate { x: 5., y: 10. },
+        )];
+        assert_eq!(want, line.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_empty_line_string() {
+        let ls: LineString<f64> = line_string![];
+        assert_eq!(Vec::<Line<f64>>::new(), ls.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_open_line_string() {
+        let ls = line_string![(x: 0., y: 0.), (x: 1., y: 1.), (x:2., y: 2.)];
+        let want = vec![
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 1., y: 1. }),
+            Line::new(Coordinate { x: 1., y: 1. }, Coordinate { x: 2., y: 2. }),
+        ];
+        assert_eq!(want, ls.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_closed_line_string() {
+        let mut ls = line_string![(x: 0., y: 0.), (x: 1., y: 1.), (x:2., y: 2.)];
+        ls.close();
+        let want = vec![
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 1., y: 1. }),
+            Line::new(Coordinate { x: 1., y: 1. }, Coordinate { x: 2., y: 2. }),
+            Line::new(Coordinate { x: 2., y: 2. }, Coordinate { x: 0., y: 0. }),
+        ];
+        assert_eq!(want, ls.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_multi_line_string() {
+        let mls = MultiLineString(vec![
+            line_string![],
+            line_string![(x: 0., y: 0.), (x: 1., y: 1.)],
+            line_string![(x: 0., y: 0.), (x: 1., y: 1.), (x:2., y: 2.)],
+        ]);
+        let want = vec![
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 1., y: 1. }),
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 1., y: 1. }),
+            Line::new(Coordinate { x: 1., y: 1. }, Coordinate { x: 2., y: 2. }),
+        ];
+        assert_eq!(want, mls.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_polygon() {
+        let p = polygon!(
+            exterior: [(x: 0., y: 0.), (x: 0., y: 10.), (x: 10., y: 10.), (x: 10., y: 0.)],
+            interiors: [
+                [(x: 1., y: 1.), (x: 1., y: 2.), (x: 2., y: 2.), (x: 2., y: 1.)],
+                [(x: 3., y: 3.), (x: 5., y: 3.), (x: 5., y: 5.), (x: 3., y: 5.)],
+            ],
+        );
+        let want = vec![
+            // exterior ring
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 0., y: 10. }),
+            Line::new(Coordinate { x: 0., y: 10. }, Coordinate { x: 10., y: 10. }),
+            Line::new(Coordinate { x: 10., y: 10. }, Coordinate { x: 10., y: 0. }),
+            Line::new(Coordinate { x: 10., y: 0. }, Coordinate { x: 0., y: 0. }),
+            // first interior ring
+            Line::new(Coordinate { x: 1., y: 1. }, Coordinate { x: 1., y: 2. }),
+            Line::new(Coordinate { x: 1., y: 2. }, Coordinate { x: 2., y: 2. }),
+            Line::new(Coordinate { x: 2., y: 2. }, Coordinate { x: 2., y: 1. }),
+            Line::new(Coordinate { x: 2., y: 1. }, Coordinate { x: 1., y: 1. }),
+            // second interior ring
+            Line::new(Coordinate { x: 3., y: 3. }, Coordinate { x: 5., y: 3. }),
+            Line::new(Coordinate { x: 5., y: 3. }, Coordinate { x: 5., y: 5. }),
+            Line::new(Coordinate { x: 5., y: 5. }, Coordinate { x: 3., y: 5. }),
+            Line::new(Coordinate { x: 3., y: 5. }, Coordinate { x: 3., y: 3. }),
+        ];
+        assert_eq!(want, p.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_multi_polygon() {
+        let mp = MultiPolygon(vec![
+            polygon!(
+                exterior: [(x: 0., y: 0.), (x: 0., y: 10.), (x: 10., y: 10.), (x: 10., y: 0.)],
+                interiors: [[(x: 1., y: 1.), (x: 1., y: 2.), (x: 2., y: 2.), (x: 2., y: 1.)]],
+            ),
+            polygon!(
+                exterior: [(x: 3., y: 3.), (x: 5., y: 3.), (x: 5., y: 5.), (x: 3., y: 5.)],
+                interiors: [],
+            ),
+        ]);
+        let want = vec![
+            // first polygon - exterior ring
+            Line::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 0., y: 10. }),
+            Line::new(Coordinate { x: 0., y: 10. }, Coordinate { x: 10., y: 10. }),
+            Line::new(Coordinate { x: 10., y: 10. }, Coordinate { x: 10., y: 0. }),
+            Line::new(Coordinate { x: 10., y: 0. }, Coordinate { x: 0., y: 0. }),
+            // first polygon - interior ring
+            Line::new(Coordinate { x: 1., y: 1. }, Coordinate { x: 1., y: 2. }),
+            Line::new(Coordinate { x: 1., y: 2. }, Coordinate { x: 2., y: 2. }),
+            Line::new(Coordinate { x: 2., y: 2. }, Coordinate { x: 2., y: 1. }),
+            Line::new(Coordinate { x: 2., y: 1. }, Coordinate { x: 1., y: 1. }),
+            // second polygon - exterior ring
+            Line::new(Coordinate { x: 3., y: 3. }, Coordinate { x: 5., y: 3. }),
+            Line::new(Coordinate { x: 5., y: 3. }, Coordinate { x: 5., y: 5. }),
+            Line::new(Coordinate { x: 5., y: 5. }, Coordinate { x: 3., y: 5. }),
+            Line::new(Coordinate { x: 3., y: 5. }, Coordinate { x: 3., y: 3. }),
+        ];
+        assert_eq!(want, mp.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_rect() {
+        let rect = Rect::new(Coordinate { x: 0., y: 0. }, Coordinate { x: 1., y: 2. });
+        let want = rect.to_polygon().lines_iter().collect::<Vec<_>>();
+        assert_eq!(want, rect.lines_iter().collect::<Vec<_>>());
+    }
+
+    #[test]
+    fn test_triangle() {
+        let triangle = Triangle(
+            Coordinate { x: 0., y: 0. },
+            Coordinate { x: 1., y: 2. },
+            Coordinate { x: 2., y: 3. },
+        );
+        let want = triangle.to_polygon().lines_iter().collect::<Vec<_>>();
+        assert_eq!(want, triangle.lines_iter().collect::<Vec<_>>());
+    }
+}
diff --git a/geo/src/algorithm/mod.rs b/geo/src/algorithm/mod.rs
index e7eb41c5ab..ce93bbcbc7 100644
--- a/geo/src/algorithm/mod.rs
+++ b/geo/src/algorithm/mod.rs
@@ -61,6 +61,8 @@ pub mod line_interpolate_point;
 pub mod line_intersection;
 /// Locate a point along a `Line` or `LineString`.
 pub mod line_locate_point;
+/// Iterate over the lines in a geometry.
+pub mod lines_iter;
 /// Apply a function to all `Coordinates` of a `Geometry`.
 pub mod map_coords;
 /// Orient a `Polygon`'s exterior and interior rings.
diff --git a/geo/src/lib.rs b/geo/src/lib.rs
index 11e5defb53..431b0796e3 100644
--- a/geo/src/lib.rs
+++ b/geo/src/lib.rs
@@ -103,6 +103,7 @@
 //!   coordinates in a geometry in-place
 //! - **[`TryMapCoords`](algorithm::map_coords::TryMapCoords)**: Map a fallible function over all
 //!   the coordinates in a geometry, returning a new geometry wrapped in a `Result`
+//! - **[`LinesIter`](algorithm::lines_iter::LinesIter)**: Iterate over lines of a geometry
 //!
 //! ## Boundary
 //!