• Language models offer a way to assign a probability to a sentence or other sequence of words, and to predict a word from preceding words. • n-grams are Markov models that estimate words from a fixed window of previous words. n-gram probabilities can be estimated by counting in a corpus and normalizing (the maximum likelihood estimate). • n-gram language models are evaluated extrinsically in some task, or intrinsically using perplexity. • The perplexity of a test set according to a language model is the geometric mean of the inverse test set probability computed by the model. • Smoothing algorithms provide a more sophisticated way to estimate the probability of n-grams. Commonly used smoothing algorithms for n-grams rely on lower-order n-gram counts through backoff or interpolation.