The ecological concept of resilience has begun to inform analysis of change in economy-environment systems. The linkages between resilience and the stability of dynamical systems are discussed, along with its role in understanding of the evolution of such systems. Particular linkages discussed include those between resilience, biodiversity and the sustainability of alternative states. Recent developments in modelling the resilience of joint economy-environment systems suggest the advantages of analysing change in the system as a Markov process, the transition probabilities between states offering a natural measure of the resilience of the system in such states. It is argued that this ‘emergent property’ of the collaboration between ecology and economics has far-reaching implications for the way we think about, model and manage the environmental sustainability of economic development.