Human activities have indirectly modified the dynamics of many populations, accelerating considerably the natural rate of species extinction and raising strong concerns about biodiversity. In many such cases, the underlying ‘natural’ dynamics of the population has been modified by human-induced increases in mortality, even if the populations are not exploited or harvested in the strict sense. Both dynamical and statistical models are needed to investigate the consequences of human-induced mortality on the overall dynamics of a population. This paper reviews existing approaches and the potential of recent developments to help form a conceptual and practical framework for analysing the dynamics of exploited populations. It examines both the simple case of an extra source of mortality instantaneously in time, and the theory involved when both risks compete over a continuous time scale. This basic theory is expanded to structured populations, using matrix population models, with applications to the conservation biology of long-lived vertebrates. The type and degree of compensation expected and approaches to detect it are reviewed, and ways of handling uncertainty are discussed.