The overriding goal of this paper is to present the most influential minimalist approaches1 to the resolution of the infinite regress in antecedent-contained deletion constructions. Therefore, the point of departure is the general description of the problem concerning the interpretation of sentences containing antecedent-contained deletion, which occurs at LF (Logical Form), when a null VP is filled with a copy of its antecedent creating at the same time an infinite regress. In the subsequent sections of this paper I strive to give an account of the attempts to resolve ACD by focusing on the theory of Vehicle Change developed by Fiengo and May (1993), the case-based approach proposed by Hornstein (1995) as well as the copy theory of movement by Fox (2002). In the last section of this paper I provide some Chomsky’s views (2004) on the direction in which the research on ACD constructions may proceed.