The concept of *persona*, originally adopted in dialogue literature, has re-surged as a promising framework for tailoring large language models (LLMs) to specific context (*e.g.*, personalized search, LLM-as-a-judge). However, the growing research on leveraging persona in LLMs is relatively disorganized and lacks a systematic taxonomy. To close the gap, we present a comprehensive survey to categorize the current state of the field. We identify two lines of research, namely (1) *LLM Role-Playing*, where personas are assigned to LLMs, and (2) *LLM Personalization*, where LLMs take care of user personas. Additionally, we introduce existing methods for LLM personality evaluation. To the best of our knowledge, we present the first survey for role-playing and personalization in LLMs under the unified view of persona. We continuously maintain a paper collection to foster future endeavors.