Quadrilateral meshes are ubiquitously used as a control grid for subdivision and parametric surfaces. The process of converting a triangular mesh into a quadrilateral is called retopology, or quadrilateral meshing, and it is an essential step for the creation of 3D models used in games, movies, and special effects. This article introduces the problem, highlights the major differences between triangular and quadrilateral meshes, and provides an overview of several new automatic and semiautomatic solutions. The pros and cons of each algorithm are discussed as well as interesting directions for future work in this area.