Platforms provide anchor-points for coordinating varied activities within an ecosystem. Understanding platform complexity and its effects is therefore a vital concern for academia and industry. The complexity defines the range of possible activities on the platform and the related aspects of control. This paper argues that abstract models of platforms used in current research remove some of the most important features underlying the inherent complexity of digital platforms. This insight is illustrated with a small study of platforms and their evolving complexity in the music industry. The exploration highlights salient phenomena that a more comprehensive theory of digital platforms should encompass. We posit that advancing theoretical perspective that better embrace the complexity of digital platforms is needed to fully capture the strategic and technological implications of emerging digital platforms.