Hidden Markov Models (HMMs) are an extremely versatile statistical representation that can be used to model any set of one-dimensional discrete symbol data. HMMs can model protein sequences in many ways, depending on what features of the protein are represented by the Markov states. For protein structure prediction, states have been chosen to represent either homologous sequence positions, local or secondary structure types, or transmembrane locality. The resulting models can be used to predict common ancestry, secondary or local structure, or membrane topology by applying one of the two standard algorithms for comparing a sequence to a model. In this chapter, we review those algorithms and discuss how HMMs have been constructed and refined for the purpose of protein structure prediction.