Although the literature contains many examples of habitat modification, there are few systematic studies of the role of such processes in the creation and maintenance of natural habitat, A key element in the development of such models is an understanding of the dynamics of the habitat modifying species, sometimes called ecosystem engineers. In this paper we present a group of strategic models of the population dynamics of a species whose ability to survive depends on modifying its own habitat. We show that such a strategy can lead either to a deterministically stable equilibrium or to endogenous cycles. We identify the conditions leading to both outcomes and discuss their interpretation in the context of examples of habitat modification to be found in the literature. We examine the feasibility of parameterising models of habitat modification from the information currently in the literature, and suggest a number of areas in which new observations or experiments would seem to be required.