The brain remains the only known example of a truly general-purpose intelligent system. The study of human and animal cognition has revealed key insights, such as the ideas of parallel distributed processing, biological vision, and learning from reward signals, that have heavily influenced the design of artificial learning systems. Many AI researchers continue to look to neuroscience as a source of inspiration and insight. A key difficulty is that neuroscience is a vast and heterogeneous area of study, encompassing a bewildering array of subfields. In this tutorial, we will seek to provide both a broad overview of neuroscience as a whole, as well as a focused look at two areas -- computational cognitive neuroscience and the neuroscience of learning in circuits -- that we believe are particularly relevant for AI researchers today. We will conclude by highlighting several ongoing lines of work that seek to import insights from these areas of neuroscience into AI, and vice versa.