Neuromorphic computing covers a diverse range of approaches to information processing all of which demonstrate some degree of neurobiological inspiration that differentiates them from mainstream conventional computing systems. The philosophy behind neuromorphic computing has its origins in the seminal work carried out by Carver Mead at Caltech in the late 1980s. This early work influenced others to carry developments forward, and advances in VLSI technology supported steady growth in the scale and capability of neuromorphic devices. Recently, a number of large-scale neuromorphic projects have emerged, taking the approach to unprecedented scales and capabilities. These large-scale projects are associated with major new funding initiatives for brain-related research, creating a sense that the time and circumstances are right for progress in our understanding of information processing in the brain. In this review we present a brief history of neuromorphic engineering then focus on some of the principal current large-scale projects, their main features, how their approaches are complementary and distinct, their advantages and drawbacks, and highlight the sorts of capabilities that each can deliver to neural modellers.