This comprehensive review explores the intersection of Large Language Models (LLMs) and cognitive science, examining similarities and differences between LLMs and human cognitive processes. We analyze methods for evaluating LLMs cognitive abilities and discuss their potential as cognitive models. The review covers applications of LLMs in various cognitive fields, highlighting insights gained for cognitive science research. We assess cognitive biases and limitations of LLMs, along with proposed methods for improving their performance. The integration of LLMs with cognitive architectures is examined, revealing promising avenues for enhancing artificial intelligence (AI) capabilities. Key challenges and future research directions are identified, emphasizing the need for continued refinement of LLMs to better align with human cognition. This review provides a balanced perspective on the current state and future potential of LLMs in advancing our understanding of both artificial and human intelligence.