  We completely classify edge-to-edge tilings of the sphere by congruent
quadrilaterals. As part of the classification, we also present a modern version
of the classification of edge-to-edge tilings of the sphere by congruent
triangles. Together with our series of papers that classifies edge-to-edge
tilings of the sphere by congruent pentagons, we complete the classification of
edge-to-edge tilings of the sphere by congruent polygons.
