Brains are, at a fundamental level, biological computing machines. They transform a torrent of complex and ambiguous sensory information into coherent thought and action, allowing an organism to perceive and model its environment, synthesize and make decisions from disparate streams of information, and adapt to a changing environment. Against this backdrop, it is perhaps not surprising that computer science, the science of building artificial computational systems, has long looked to biology for inspiration. However, while the opportunities for cross-pollination between neuroscience and computer science are great, the road to achieving brain-like algorithms has been long and rocky. Here, we review the historical connections between neuroscience and computer science, and we look forward to a new era of potential collaboration, enabled by recent rapid advances in both biologically-inspired computer vision and in experimental neuroscience methods. In particular, we explore where neuroscience-inspired algorithms have succeeded, where they still fail, and we identify areas where deeper connections are likely to be fruitful.