Neuromorphic computing is becoming a popular approach for implementations of brain-inspired machine learning tasks. As a paradigm for both hardware and algorithm design, neuromorphic computing aims to emulate several aspects related to the structure and function of the biological nervous system to achieve artificial intelligence with efficiencies that are orders of magnitude better than those exhibited by general-purpose computing hardware. We provide a holistic treatment of spike-based neuromorphic computing (i.e., based on spiking neural networks), detailing biological motivation, key aspects of neuromorphic algorithms, and a survey of state-of-the-art neuromorphic hardware. In particular, we focus on these aspects within the context of brain-inspired vision applications. Our aim is to serve as a complement to several of the existing reviews on neuromorphic computing while also providing a unique perspective.