The Voyager 2 flybys of Uranus and Neptune revealed the first multipolar planetary magnetic fields and highlighted how much we have yet to learn about ice giant planets. In this review, we summarize observations of Uranus' and Neptune's magnetic fields and place them in the context of other planetary dynamos. The ingredients for dynamo action in general, and for the ice giants in particular, are discussed, as are the factors thought to control magnetic field strength and morphology. These ideas are then applied to Uranus and Neptune, where we show that no models are yet able to fully explain their observed magnetic fields. We then propose future directions for missions, modelling, experiments and theory necessary to answer outstanding questions about the dynamos of ice giant planets, both within our solar system and beyond. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.
Keywords: Neptune; Uranus; dynamo; ice giant planets; interiors; magnetic fields.