Heat, strain, topography and atmospheric emissions associated with volcanism are well observed by satellites orbiting the Earth. Gravity and electromagnetic transients from volcanoes may also prove to be measurable from space. The nature of eruptions means that the best strategy for measuring their dynamic properties remotely from space is to employ two modes with different spatial and temporal samplings: eruption mode and background mode. Such observational programmes are best carried out at local or regional volcano observatories by coupling them with numerical models of volcanic processes. Eventually, such models could become multi–process, operational forecast models that assimilate the remote and other observables to constrain their uncertainties. The threat posed by very large magnitude explosive eruptions is global and best addressed by a spaceborne observational programme with a global remit.