As AI systems become increasingly powerful, the need for safe AI has become more pressing. Humans are an attractive model for AI safety: as the only known agents capable of general intelligence, they perform robustly even under conditions that deviate significantly from prior experiences, explore the world safely, understand pragmatics, and can cooperate to meet their intrinsic goals. Intelligence, when coupled with cooperation and safety mechanisms, can drive sustained progress and well-being. These properties are a function of the architecture of the brain and the learning algorithms it implements. Neuroscience may thus hold important keys to technical AI safety that are currently underexplored and underutilized. In this roadmap, we highlight and critically evaluate several paths toward AI safety inspired by neuroscience: emulating the brain's representations, information processing, and architecture; building robust sensory and motor systems from imitating brain data and bodies; fine-tuning AI systems on brain data; advancing interpretability using neuroscience methods; and scaling up cognitively-inspired architectures. We make several concrete recommendations for how neuroscience can positively impact AI safety.