This report explores the development of exploitation theory in mathematical Marxian economics by reviewing the main controversies surrounding the proper definition of exploitation since the contribution of Okishio(1963). The report first examines the debates on the Fundamental Marxian Theorem and Class-Exploitation Correspondence Principle, developed mainly in the 1970s and 1980s, followed by the property relation theory of exploitation by Roemer (1982). Then, the more recent exploitation theory proposed by Vrousalis (2013) and Wright (2000) is introduced. Finally, the report introduces and comments on recent axiomatic studies of exploitation by focusing on the work of Veneziani and Yoshihara (2015a).