Current artificial intelligence (AI) models often focus on enhancing performance through meticulous parameter tuning and optimization techniques. However, the fundamental design principles behind these models receive comparatively less attention, which can limit our understanding of their potential and constraints. This comprehensive review explores the diverse design inspirations that have shaped modern AI models, i.e., brain-inspired artificial intelligence (BIAI). We present a classification framework that categorizes BIAI approaches into physical structure-inspired and human behavior-inspired models. We also examine the real-world applications where different BIAI models excel, highlighting their practical benefits and deployment challenges. By delving into these areas, we provide new insights and propose future research directions to drive innovation and address current gaps in the field. This review offers researchers and practitioners a comprehensive overview of the BIAI landscape, helping them harness its potential and expedite advancements in AI development.