A model for sequences where the thing you care about is hidden and you only see its effects. You observe the words in a sentence and want the grammatical roles behind them, or you observe sounds and want the words. It ran speech recognition and sequence tagging for decades before neural methods arrived.
Technical view
Comprises hidden states with Markov transitions and observation likelihoods, with the Viterbi algorithm for the most likely state sequence, the forward-backward algorithm for marginals, and Baum-Welch for unsupervised parameter estimation. Displaced by neural sequence models, but the framing survives in structured prediction, and the state space model architectures now competing with transformers are a direct descendant.
Related
Part of AI Terminology Index, section: Classical Machine Learning.