This chapter reviews the core concepts of complexity science and legal scholars' application of the theories to the law. There have been three major themes in this body of scholarship. First, a descriptive body of work has focused on mapping complexity science concepts onto legal systems to enable explanation of legal systems as complex adaptive systems. Second, a prescriptive thrust has moved from mapping concepts towards developing principles for structural design and normatively acceptable operation of legal systems given their complex adaptive system properties. Finally, an ethical focus in the literature explores what it means to be an actor in a complex legal system. The chapter then shifts to the empirical front, identifying potentially useful metrics and methods for studying legal complexity. It presents a proposal for monitoring legal complexity over time by conceptualising what we call Legal Maps – a multilayered, Google Maps–style active representation of the legal system network at work.