The spatial distribution of a species is determined by dynamic processes such as reproduction, mortality and dispersal. Conventional static species distribution models (SDMs) do not incorporate these processes explicitly. This limits their applicability, particularly for non-equilibrium situations such as invasions or climate change. In this paper we show how dynamic SDMs can be formulated and fitted to data within a Bayesian framework. Our focus is on discrete state-space Markov process models which provide a flexible framework to account for stochasticity in key demographic processes, including dispersal, growth and competition. We show how to construct likelihood functions for such models (both discrete and continuous time versions) and how these can be combined with suitable observation models to conduct Bayesian parameter inference using computational techniques such as Markov chain Monte Carlo. We illustrate the current state-of-the-art with three contrasting examples using both simulated and empirical data. The use of simulated data allows the robustness of the methods to be tested with respect to deficiencies in both data and model. These examples show how mechanistic understanding of the processes that determine distribution and abundance can be combined with different sources of information at a range of spatial and temporal scales. Application of such techniques will enable more reliable inference and projections, e.g. under future climate change scenarios than is possible with purely correlative approaches. Conversely, confronting such process-oriented niche models with abundance and distribution data will test current understanding and may ultimately feedback to improve underlying ecological theory.