One of Bishop’s six mathematical activities is playing which includes modelling, hypothetical thinking and abstraction. These can be in young children’s play, but do they by their presence make this play mathematical? In this chapter, we explore this question by first defining play and then comparing its features with what is known about mathematicians’ academic play and how mathematics education researchers have described young children’s play. From this theoretical discussion, we discuss the features of play, which can enable it to be described as mathematical. We use these features to analyse a small episode of children playing to discuss if and how their play could be considered to be mathematical