This survey explores the potential of hallucinations in large language models (LLMs) as a source of creativity, challenging the traditional view of hallucinations as solely detrimental. It begins by reviewing the taxonomy of hallucinations and their negative impact on LLM reliability, particularly in critical applications. The survey then delves into historical examples and recent theories to explore the creative benefits of hallucinations in LLMs. It discusses the definitions and assessment methods of creativity, emphasizing the importance of divergent and convergent thinking phases in transforming and harnessing hallucinations for creativity. The paper concludes by discussing future research directions, highlighting the need to further explore and refine the application of hallucinations in creative processes within LLMs. The survey provides a comprehensive overview of the current state of research and suggests that while hallucinations can be harmful, they also hold the potential to enhance creativity in LLMs.This survey explores the potential of hallucinations in large language models (LLMs) as a source of creativity, challenging the traditional view of hallucinations as solely detrimental. It begins by reviewing the taxonomy of hallucinations and their negative impact on LLM reliability, particularly in critical applications. The survey then delves into historical examples and recent theories to explore the creative benefits of hallucinations in LLMs. It discusses the definitions and assessment methods of creativity, emphasizing the importance of divergent and convergent thinking phases in transforming and harnessing hallucinations for creativity. The paper concludes by discussing future research directions, highlighting the need to further explore and refine the application of hallucinations in creative processes within LLMs. The survey provides a comprehensive overview of the current state of research and suggests that while hallucinations can be harmful, they also hold the potential to enhance creativity in LLMs.