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 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 dynamos. We then propose future directions for
missions, modeling, experiments, and theory necessary to answer
outstanding questions about the dynamos of ice giant planets, both
within our solar system and beyond.