The superrotation of the atmospheres of Venus and Titan has puzzled dynamicists for many years and seems to put these planets in a very different dynamical regime from most other planets. In this review, we consider how to define superrotation objectively and explore the constraints that determine its occurrence. Atmospheric superrotation also occurs elsewhere in the Solar System and beyond, and we compare Venus and Titan with Earth and other planets for which wind estimates are available. The extreme superrotation on Venus and Titan poses some difficult challenges for numerical models of atmospheric circulation, much more difficult than for more rapidly rotating planets such as Earth or Mars. We consider mechanisms for generating and maintaining a superrotating state, all of which involve a global meridional overturning circulation. The role of nonaxisymmetric eddies is crucial, however, but the detailed mechanisms may differ between Venus, Titan, and other planets.