The progress of brain cognition and learning mechanisms has provided new inspiration for the next generation of artificial intelligence (AI) and provided the biological basis for the establishment of new models and methods. Brain science can effectively improve the intelligence of existing models and systems. Compared with other reviews, this article provides a comprehensive review of brain-inspired deep learning algorithms for learning, perception, and cognition from microscopic, mesoscopic, macroscopic, and super-macroscopic perspectives. First, this article introduces the brain cognition mechanism. Then, it summarizes the existing studies on brain-inspired learning and modeling from the perspectives of neural structure, cognitive module, learning mechanism, and behavioral characteristics. Next, this article introduces the potential learning directions of brain-inspired learning from four aspects: perception, cognition, understanding, and decision-making. Finally, the top-ten open problems that brain-inspired learning, perception, and cognition currently face are summarized, and the next generation of AI technology has been prospected. This work intends to provide a quick overview of the research on brain-inspired AI algorithms and to motivate future research by illuminating the latest developments in brain science.