Understanding an animal’s behaviors (e.g., foraging, resting) is essential to predicting their response to environmental change. However, direct observations of these behaviors are often difficult to gather, and instead ecologists increasingly collect movement-related data (e.g., GPS tracks, high-frequency time series of 3D acceleration). Here, we will show that Hidden Markov models (HMMs) are ideal tools to infer behavioral processes from movement observations that are regularly spaced in time. Movement HMMs model at least two components: a multivariate time series of observations and an underlying hidden sequence of discrete states used to represent the behaviors of interest. HMMs are now ubiquitously used in movement ecology, but most applications are limited to simple models. Our recent work focuses on extending HMMs to model state transitions and emission probabilities as functions of spatially-varying covariates and account for complex temporal correlation. Using movement data from species such as the polar bear, we will show how HMMs can provide ecological insights that would be otherwise difficult to achieve. These extensions are transferable to applications beyond ecology.