Comparatively little is known about atmospheric chemistry on Uranus and Neptune, because remote spectral observations of these cold, distant `Ice Giants' are challenging, and each planet has only been visited by a single spacecraft during brief flybys in the 1980s. Thermochemical equilibrium is expected to control the composition in the deeper, hotter regions of the atmosphere on both planets, but disequilibrium chemical processes such as transport-induced quenching and photochemistry alter the composition in the upper atmospheric regions that can be probed remotely. Surprising disparities in the abundance of disequilibrium chemical products between the two planets point to significant differences in atmospheric transport. The atmospheric composition of Uranus and Neptune can provide critical clues for unravelling details of planet formation and evolution, but only if it is fully understood how and why atmospheric constituents vary in a three-dimensional sense and how material coming in from outside the planet affects observed abundances. Future mission planning should take into account the key outstanding questions that remain unanswered about atmospheric chemistry on Uranus and Neptune, particularly those questions that pertain to planet formation and evolution, and those that address the complex, coupled atmospheric processes that operate on Ice Giants within our solar system and beyond. This article is part of a discussion meeting issue `Future exploration of ice giant systems'.