The Internet is a universal source of information for its users. However, obtaining desired content has become the main focus of interest rather than the communication with machine endpoints. The increased availability of mobile devices makes such desired access continuous in time and space, adding an extra dimension and level of complexity for satisfying users' needs. Together with the almost ubiquitous availability of computing and storage resources, this has led to efforts that focus on disseminating information to a possibly changing set of consumers. In this paper, we revisit several strands of IP mobility work with respect to the benefit when being seen from an information-centric networking (ICN) angle. We present a set of architecture invariants together with a functional model, both of which allow for formulating the various concepts of mobility from an ICN angle. We furthermore present and evaluate two approaches to support mobility in ICN, a proactive one based on prefetching subscriptions to possible reconnection points of a mobile node and a reactive one based on buffer relocation. Finally, we also outline various challenges in evaluating such approaches, these challenges caused by the paradigm change that ICN constitutes.