In this chapter, we survey some recent contributions analyzing oligopoly theory and product differentiation from the viewpoint of models of localized competition. In other words, we exclude from our analysis the field of monopolistic competition (see Thisse and Uschev, Chapter 5 in this Handbook) and oligopoly theory as in the neoclassical vein (Vives, 2000). We start by recalling some elements of the microeconomic theory of consumer demand based on characteristics, as introduced by Lancaster (1966). Then, we present successively the theory of horizontal product differentiation, based on the article by Hotelling (1929) and the theory of vertical product differentiation, based on the article by Gabszewicz and Thisse (1979). Then, we develop a model nesting both horizontal and vertical product differentiation (Gabszewicz and Wauthy, 2012). Finally, we propose two applications of this approach, one based on network externalities and the other on environmental economics.