Neuroscience and brain-inspired artificial intelligence are significant research areas. Many countries have launched brain-related projects in which neuroscience and brain-inspired artificial intelligence are major targeted areas to increase national interests and enhance their strength in key areas such as military and homeland security in the competitive global world. Methods, emerging technologies, and progress in neuroscience and brain-inspired artificial intelligence are introduced in this paper that specifically include brain-inspired computing, brain association graph, brain networks, the connectome, brain reconstruction, imaging technologies used for the brain, chips and devices inspired by the human brain, brain-computer interface or brain-machine interfaces, cyborg, neuro-robotics, and quantum robotics. Challenges in some of the topics are also presented and discussed.