Lifelong learning - an agent's ability to learn throughout its lifetime - is a hallmark of biological learning systems and a central challenge for artificial intelligence (AI). The development of lifelong learning algorithms could lead to a range of novel AI applications, but this will also require the development of appropriate hardware accelerators, particularly if the models are to be deployed on edge platforms, which have strict size, weight, and power constraints. Here, we explore the design of lifelong learning AI accelerators that are intended for deployment in untethered environments. We identify key desirable capabilities for lifelong learning accelerators and highlight metrics to evaluate such accelerators. We then discuss current edge AI accelerators and explore the future design of lifelong learning accelerators, considering the role that different emerging technologies could play.