This paper provides a comprehensive survey of Chain-of-X (CoX) methods for Large Language Models (LLMs), which extend the concept of Chain-of-Thought (CoT) to address various challenges across diverse domains and tasks. CoX methods are categorized by taxonomies of nodes and application tasks, including Chain-of-Intermediates, Chain-of-Augmentation, Chain-of-Feedback, and Chain-of-Models. The paper discusses the findings and implications of existing CoX methods and explores potential future directions. CoX methods have been applied to tasks such as multi-modal interaction, hallucination reduction, planning with LLM-based agents, and evaluation tools. The survey aims to serve as a detailed and up-to-date resource for researchers seeking to apply the idea of CoT to broader scenarios.This paper provides a comprehensive survey of Chain-of-X (CoX) methods for Large Language Models (LLMs), which extend the concept of Chain-of-Thought (CoT) to address various challenges across diverse domains and tasks. CoX methods are categorized by taxonomies of nodes and application tasks, including Chain-of-Intermediates, Chain-of-Augmentation, Chain-of-Feedback, and Chain-of-Models. The paper discusses the findings and implications of existing CoX methods and explores potential future directions. CoX methods have been applied to tasks such as multi-modal interaction, hallucination reduction, planning with LLM-based agents, and evaluation tools. The survey aims to serve as a detailed and up-to-date resource for researchers seeking to apply the idea of CoT to broader scenarios.