With the influx of complex and detailed tracking data gathered from\nelectronic tracking devices, the analysis of animal movement data has recently\nemerged as a cottage industry amongst biostatisticians. New approaches of ever\ngreater complexity are continue to be added to the literature. In this paper,\nwe review what we believe to be some of the most popular and most useful\nclasses of statistical models used to analyze individual animal movement data.\nSpecifically we consider discrete-time hidden Markov models, more general\nstate-space models and diffusion processes. We argue that these models should\nbe core components in the toolbox for quantitative researchers working on\nstochastic modelling of individual animal movement. The paper concludes by\noffering some general observations on the direction of statistical analysis of\nanimal movement. There is a trend in movement ecology toward what are arguably\noverly-complex modelling approaches which are inaccessible to ecologists,\nunwieldy with large data sets or not based in mainstream statistical practice.\nAdditionally, some analysis methods developed within the ecological community\nignore fundamental properties of movement data, potentially leading to\nmisleading conclusions about animal movement. Corresponding approaches, e.g.\nbased on L\\'evy walk-type models, continue to be popular despite having been\nlargely discredited. We contend that there is a need for an appropriate balance\nbetween the extremes of either being overly complex or being overly simplistic,\nwhereby the discipline relies on models of intermediate complexity that are\nusable by general ecologists, but grounded in well-developed statistical\npractice and efficient to fit to large data sets.\n