Large language models (LLMs) have demonstrated strong capabilities across diverse tasks such as language understanding, reasoning, planning, and code generation. However, their sequence-based architectures limit their ability to capture complex relational structures, long-range dependencies, and multi-hop interactions. Graphs, which explicitly model entities and relationships, provide a natural complement to LLMs by enabling structured representation, multi-hop reasoning, and improved knowledge grounding. This synergy has led to a growing body of research on graph-enhanced LLMs, which we refer to as Graph4LLM. In this survey, we present a systematic, pipeline-oriented review of Graph4LLM methods, categorizing them into three stages of the LLM pipeline: (1) the input phase, where graphs structure prompts and incorporate external knowledge; (2) the model phase, where graphs guide word-level representations and agent-level coordination; and (3) the output phase, where graphs support structured reasoning, planning, and verification. For each phase, we provide a detailed review of the key methods and techniques. We further present a broad range of application scenarios, organizing them into general and domain-specific applications, and highlight how Graph4LLM methods demonstrate strong potential across diverse tasks and real-world settings. Finally, we outline the challenges and future research directions for developing more efficient and interpretable solutions. Resources for Graph4LLM are available at https://github.com/BUPT-GAMMA/Awesome-Graph4LLM.