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Collaborative filtering (CF) methods produce recommendations based on usage patterns without the need of exogenous information about items or users. CF algorithms have shown great prediction quality both in academic research and in industrial applications. This chapter surveys core methods in the field. Matrix factorization techniques, which became a first choice for implementing CF, are described together with other innovations. We also describe several extensions that bring competitive accuracy into neighborhood methods, which used to dominate the field. The chapter demonstrates how to utilize temporal models and implicit feedback to extend model accuracy. In passing, we illustrate the use of CF algorithms on the Netflix Prize competition. The CF methods discussed in this chapter have been proposed a decade ago but still show state-of-the art accuracy in recent studies. The modeling patterns …