This chapter discusses the major types of matrix models, a rich and multifarious family of distributional semantic models (DSMs) that extend and generalize the vector space model in information retrieval from which they derive the use of co-occurrence matrices to represent distributional information. We first focus on a group of matrix DSMs (e.g., Latent Semantic Analysis) that we refer to as classical models, since they directly implement the basic procedure to build distributional representations introduced in Chapter 2. Then, we present DSMs that propose extensions and variants to classical ones. Latent Relational Analysis uses pairs of lexical items as targets to measure the semantic similarity of the relations between them. Distributional Memory represents distributional data with a high-order tensor, from which different types of co-occurrence matrices are derived to address various semantic tasks. Topic Models and GloVe introduce new approaches to reduce the dimensionality of the co-occurrence matrix, respectively based on probabilistic inference and a method strongly inspired by neural DSMs.