This chapter describes how hidden Markov models (HMM) can be used to model movement data, and demonstrates the implementation thereof in some case studies, related to the movement of larvae of the fruit fly Drosophila melanogaster, to the movement of a bison and to the movement of several groups of red-cockaded woodpeckers. For flexible modelling of data on step lengths and turning angles using HMMs, a class of building-blocks can be considered that comprises correlated and biased random walks (CRW and BRW) as well as walks that are both correlated and biased (BCRWs). A typical HMM for animal movement will involve some combination of CRWs, BRWs and BCRWs, each of these being allocated to a different state of the underlying Markov chain. HMMs for animal movement data typically involve the assumption of contemporaneous conditional independence.