The aim of this paper is to explore and review current understanding of the potential of computer play to enhance young children’s cognitive development, as compared to the developmental value of traditional make-believe play in which children spontaneously engage during their early childhood years. Theories of play have identified many ways in which traditional play may advance children’s cognitive, social and emotional development. Recently, much traditional childhood play is being replaced by time spent on computer play, and often from a very early age. To produce software that is appealing to young children, designers aim to present content in a play-oriented manner to attract and sustain children's attention. However, computer programs are often produced atheoretically for cosmetic appeal, using animations, colour, sound, and surprise as the basis of their design, rather than pedagogical principles or developmental theories of play. This research attempts to analyse the ways that knowledge of the developmental value of spontaneous play established in conventional play settings can be applied to the theoretical basis of computer play design for young children. Moreover, it is argued that computer play, if designed appropriately, might comprise some developmental potential which can go beyond that of traditional spontaneous play. In particular, it is hypothesized that the foundation for further development of higher order thinking skills such as complex systems of abstract, logic and sign-mediated operations and symbolic representation, can be established and reinforced by purposefully designed computer play.