For the past decade, economic geography and spatial analysis are dominated by the "New economic geography" (NEG). This school of thought is characterized by its focus on economies of scale (both external and internal) in the production process, but also by its emphasis on imperfect competition. The NEG has already had a profound impact on economists and geographers alike, but at the same time has been under attack by a number of scholars on the basis that even though the NEG has criticised traditional economic geography and regional science, it suffers by the same formalism and detachment from reality. This paper presents the basic concepts of the NEG. Its critique, and a comparison between new economic geography and the alternative framework of Sheppard and Barnes, who tried to use a mixture of the mathematical formalism of analytical Marxism and neo-ricardian concepts of space.