Resources are produced in pulses in many terrestrial environments, and have important effects on the population dynamics and assemblage structure of animals that consume them. Resource-pulsing is particularly dramatic in Australian desert environments owing to marked spatial and temporal variability in rainfall, and thus primary productivity. Here, we first review how Australia's desert mammals respond to fluctuations in resource production, and evaluate the merits of three currently accepted models (the ecological refuge, predator refuge and fire-mosaic models) as explanations of the observed dynamics. We then integrate elements of these models into a novel state-and-transition model and apply it to well-studied small mammal assemblages that inhabit the vast hummock grassland, or spinifex, landscapes of the continental inland. The model has four states that are defined by differences in species composition and abundance, and eight transitions or processes that prompt shifts from one state to another. Using this model as a template, we construct three further models to explain mammalian dynamics in cracking soil habitats of the Lake Eyre Basin, gibber plains of the Channel Country, and the chenopod shrublands of arid southern Australia. As non-equilibrium concepts that recognise the strongly intermittent nature of resource pulsing in arid Australia, state-and-transition models provide useful descriptors of both spatial and temporal patterns in mammal assemblages. The models should help managers to identify when and where to implement interventions to conserve native mammals, such as control burns, reduced grazing or predator management. The models also should improve understanding of the potential effects of future climate change on mammal assemblages in arid environments in general. We conclude by proposing several tests that could be used to refine the models and guide further research.