Ernest Mandel theorised the capitalist world economy as an articulated system of capitalist, semi-capitalist and precapitalist relations of production, linked to each other by capitalist relations of exchange and domination by the capitalist world market. This seems to be an interesting starting point for an historically well-founded theory, building on and going beyond Marx's work, of the worldwide expansion of the capitalist mode of production from its origins to the present. In his attempt to formulate his theory, Mandel did not succeed in resolving all difficulties, however. His main works – Marxist Economic Theory and Late Capitalism – show a number of dangling loose ends. The central question is whether these loose ends are merely technical difficulties or whether they reveal fatal flaws in the theory as a whole. In order to come a step closer to answering this question, a conference was organised in Amsterdam, November 2003. This introduction formulates the five, closely interrelated issues that were highlighted at this conference.