Psychological insights have long shaped pivotal NLP breakthroughs, from attention mechanisms to reinforcement learning and social modeling. As Large Language Models (LLMs) develop, there is a rising consensus that psychology is essential for capturing human-like cognition, behavior, and interaction. This paper reviews how psychological theories can inform and enhance stages of LLM development. Our review integrates insights from six subfields of psychology, including cognitive, developmental, behavioral, social, personality psychology, and psycholinguistics. With stage-wise analysis, we highlight current trends and gaps in how psychological theories are applied. By examining both cross-domain connections and points of tension, we aim to bridge disciplinary divides and promote more thoughtful integration of psychology into NLP research.