A hidden Markov model (HMM) is for inferring hidden states of a Markov model based on observed data. For example, introns and exons are hidden states and need to be inferred from the observed nucleotide sequences. Similarly, secondary structural elements such as alpha helices and beta sheets are hidden states and need to be inferred from observed amino acid sequences. The accuracy of HMM in inferring hidden states depends on the transition probability matrix and emission probability matrix derived from training HMM with representative observations. If different states have very different probabilities to transit into each other, and if the emission probability matrices of the hidden states are highly different from each other, then HMM can be quite accurate. This chapter details the key algorithms used in HMM, such as the Viterbi algorithm for reconstructing the hidden states and the forward algorithm to compute the probability of the observed sequence of events. Both the Viterbi and forward algorithms are dynamic programming algorithms that we were first exposed to in the chapter on sequence alignment. HMM is applied to reconstructing protein secondary structure as an illustrative example.