The ice giant planets provide some of the most interesting natural laboratories for studying the influence of large obliquities, rapid rotation, highly asymmetric magnetic fields and wide-ranging Alfvénic and sonic Mach numbers on magnetospheric processes. The geometries of the solar wind-magnetosphere interaction at the ice giants vary dramatically on diurnal timescales due to the large tilt of the magnetic axis relative to each planet's rotational axis and the apparent off-centred nature of the magnetic field. There is also a seasonal effect on this interaction geometry due to the large obliquity of each planet (especially Uranus). With in situ observations at Uranus and Neptune limited to a single encounter by the Voyager 2 spacecraft, a growing number of analytical and numerical models have been put forward to characterize these unique magnetospheres and test hypotheses related to the magnetic structures and the distribution of plasma observed. Yet many questions regarding magnetospheric structure and dynamics, magnetospheric coupling to the ionosphere and atmosphere, and potential interactions with orbiting satellites remain unanswered. Continuing to study and explore ice giant magnetospheres is important for comparative planetology as they represent critical benchmarks on a broad spectrum of planetary magnetospheric interactions, and provide insight beyond the scope of our own Solar System with implications for exoplanet magnetospheres and magnetic reversals. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.