The breaking apart of magma into fragments is intimately related to the eruptive style and thus the nature and footprint of volcanic hazards. The size and shape distributions of the fragments, in turn, affect the efficiency of heat transfer within pyroclastic plumes and currents and the settling velocity, and so the residence time, of particles in the atmosphere. Fundamental work relating the glass transition to the fragmentation of magmas remains at the heart of conceptual and numerical models of volcanic eruptions. Current fragmentation criteria, however, do not predict the sizes and shapes of the resulting fragments, or fully account for the multiphase nature of magmas or ways in which magma can break in a fluidal manner or by thermal stress. The pulsatory, non-steady state nature of some eruptions, and related interactions with these fragmentation criteria, also requires further investigation. Here, we briefly review some recent advances in the field of magma fragmentation and provide a perspective on how integrated field, experimental and numerical modelling studies can address key outstanding challenges.