Movement data from marine animals tagged with electronic tags are becoming increasingly diverse and plentiful. This trend entails a need for statistical methods that are able to filter the observations to extract the ecologically relevant content. This dissertation focuses on the development and application of hidden Markov models (HMMs) for analysis of movement data from sh. The main contributions are represented by six scientific publications. Estimation of animal location from uncertain and possibly indirect observations is the starting point of most movement data analyses. In this work a discrete state HMM is employed to deal with this task. Specifically, the continuous horizontal plane is discretised into grid cells, which enables a state-space model for the geographical location to be estimated on this grid. The estimation model for location is extended with an additional state representing the behaviour of the animal. With the extended model can migratory and resident movement behaviour be related to geographical regions. For population inference multiple individual state-space analyses can be interconnected using mixed effects modelling. This framework provides parameter estimates at the population level and allows ecologists to identify individuals that deviate from the rest of the tagged population. The thesis also deals with geolocation on state-spaces with complicated geometries. Using an unstructured discretisation and the finite element method tortuous shore line geometries are closely approximated. This furthermore enables accurate probability densities of location to be computed. Finally, the performance of the HMM approach in analysing nonlinear state space models is compared with two alternatives: the AD Model Builder framework and BUGS, which relies on Markov chain Monte Carlo estimation.