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This paper provides an innovative axiomatic analysis of the notion of exploitation as the unequal exchange of labour, focusing on the relation between exploitation and profits. General convex economies with heterogeneous agents endowed with unequal amounts of physical and human capital are considered. An axiomatic characterisation of the class of definitions that preserve the Fundamental Marxian Theorem (FMT) in this general context is derived. It is shown that none of the main received definitions preserves the FMT. Instead, a definition related to the `New Interpretation' (Dumenil, 1980; Foley, 1982) is presented which preserves the FMT and allows one to generalise a number of key insights of exploitation theory to complex advanced economies.