Among the issues pertaining to the problem of personal identity, as one of the fundamental questions in the philosophy of punishment, is the need to establish, prior to determining the rationale, modalities, and purposes of punishment, the relationship between the agent of the crime at the time of its commission and the person who is presently the subject of punishment. Establishing this relationship, in turn, requires elucidating the connection between the mutability of the “self,” the persistence of personal identity, and the possibility of attributing criminal responsibility. Accordingly, adopting an analytic-philosophical approach and drawing upon library-based sources, the present study seeks to examine various perspectives on personal identity and to assess their implications for criminal responsibility. The findings demonstrate that neither a criterion of absolute bodily or psychological continuity nor memory or consciousness, considered in isolation, is sufficient to establish the persistence of personal identity and the attribution of criminal responsibility. Rather, it is both possible and necessary to posit a form of relative and multidimensional continuity encompassing bodily, psychological, and causal dimensions. On this basis, the persistence of personal identity should be regarded not as an independent ground for the justification of punishment, but rather as a preliminary condition for the attribution of criminal responsibility. Accordingly, the degree to which such continuity is attenuated may affect the possibility and scope of the imposition of punishment, without necessarily entailing a direct relationship between changes in personal identity and the severity of punishment.