Abstract This article opens a window on linguistic creativity through an in-depth discussion of language play. To this aim, language play is initially conceptualized from a socio-cognitive perspective. ‘Language play for fun’ and ‘language play for practice’ as two dominant approaches in the relevant literature are, then, touched upon. Afterward, the paper elucidates how language play, in its various manifestations, can inform and influence linguistic creativity. In this respect, a theoretical (linguistic) and a socio-pragmatic perspective are presented. In particular, the paper addresses the possibility of playing to ‘language’ outside the box (i.e., to go beyond the conventional systemic constraints of language). Highlighting the ubiquity of language play, it also considers Wittgenstein’s notion of ‘language games’ (or Sprachspiele). Furthermore, the performative power of playful creativity to make and ‘unmake’ language in society is elaborated on. The article contends that language play may offer valuable insights to extend the borders of linguistic creativity. This argument is further developed under the purview of ‘complexity theory,’ ‘soft computing,’ and ‘computational linguistic creativity.’ Finally, the paper advocates an ‘integrated science’ approach to advance play-based research on linguistic creativity.