Ideas, policies and models related to criminal justice often travel between places. How, then, should we make sense of this movement? We make the case for drawing on the policy mobilities literature, which originates in human geography. It is only recently that criminological studies have drawn on small parts of this literature. This article argues for a more expansive engagement with the policy mobilities literature, so that criminal justice researchers focus on concepts such as mobilities, mutation, assemblages, learning, educating and showcasing when studying the movement of criminal justice ideas, policies and models. To illustrate our argument, we will draw on a case study of the adaptation of the ‘Swedish model’ of governing sex work by policymakers in Northern Ireland.