Diverse subfields of neuroscience have enriched artificial intelligence for many decades. With recent advances in machine learning and artificial neural networks, many neuroscientists are partnering with AI researchers and machine learning experts to analyze data and construct models. This paper attempts to demonstrate the value of such collaborations by providing examples of how insights derived from neuroscience research are helping to develop new machine learning algorithms and artificial neural network architectures. We survey the relevant neuroscience necessary to appreciate these insights and then describe how we can translate our current understanding of the relevant neurobiology into algorithmic techniques and architectural designs. Finally, we characterize some of the major challenges facing current AI technology and suggest avenues for overcoming these challenges that draw upon research in developmental and comparative cognitive neuroscience.