<p>To begin exploring how children’s play can support the development of the foundations of mathematics learning, we outline the landscape of play and mathematics. We introduce two debates concerning play and math, the resolution of which could advance the field. Because the main issue is the type(s) of play that should be encouraged, we provide a taxonomy of play that illustrates the contributions each category can make to early mathematics education. The questions we consider include: What mathematics does or could potentially emerge from distinct play contexts? What opportunities do different types of play offer teachers and children to develop implicit or explicit representations of mathematics? For each type, how can engaging in playful activities foster conceptual learning and extend learning beyond mathematics, including the synergistic relationship between play and mathematics? Although this is not a systematic review but a narrative and conceptual analysis, we base our findings on key literature supporting and clarifying our conclusions in each section.</p>