In this article, we present an overview of methods for sequential simulation from posterior distributions.

These methods are of particular interest in Bayesian filtering for discrete time dynamic models

that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed

that unifies many of the methods which have been proposed over the last few decades in several

different scientific disciplines. Novel extensions to the existing methods are also proposed.We showin

particular how to incorporate local linearisation methods similar to those which have previously been

employed in the deterministic filtering literature these lead to very effective importance distributions.

Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of

the analytic structure present in some important classes of state-space models. In a final section we

develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.