The complexity of the bonds between the individuals and its environment in the social context was transformed through the postmodern rupture that leads to the conception of subject whose identity is linked to networks and technology platforms. In the same orientation, art has developed a branched speech on the theme of identity and new media that focuses on the conceptualization of the postmodern subject, reaffirming the impact and importance of virtual technology and everyday life in contemporary being. This paper analyzes the question about in what extent the postmodern paradigm determines the construction or deconstruction of the identity in the social relationships in nowadays society following the theoretical contextualization of the proposals from the constructivism of Vygotsky and the deconstruction of Derrida. We explore questions about cultural identity and representation as a social construct and how contemporary art has been inserting this discourses in their practices, considering contemporary art proposals that work with the identity of individuals in our social context, following forms of critique and resistance in art with the case of studies of artists working with Appropriation art and deconstruction like Cindy Sherman and Richard Prince. This reflection and theoretical analysis is in relation to the discussion of the issue of identity through artistic perspective in the digital and new media society and is inserted into the research of the MA in arts management and production from the University of Murcia.