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The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.