Large language models (LLMs) have made progress in knowledge-intensive tasks, reasoning and planning, and collaborative problem solving, yet they exhibit intrinsic limitations such as knowledge cutoff, single-threaded reasoning that hinders finer-grained branch and aggregation, and rigid collaboration mechanisms that struggle to coordinate specialized capabilities. Graphs, with their ability to represent relational knowledge and complex dependencies, offer a natural means to address these limitations: they provide structured, high-density knowledge for augmenting or correcting LLMs’ generation; enable revisitable inference by organizing intermediate steps as graphs; and support dynamic coordination among experts or agents in collaborative settings. Motivated by these developments, we present the first systematic survey of graph-assisted LLMs from the perspective of how graph structures mitigate LLMs’ limitations. We introduce a taxonomy spanning *Graph-Assisted Knowledge Augmentation*, *Graph-Assisted Reasoning and Planning*, and *Graph-Assisted LLM Collaboration*, and analyze representative methods, summarize common design patterns, and outline open challenges and future directions for advancing LLMs with graph-based enhancements. The collected papers are available in [link here](https://github.com/FairyFali/Graph4LLM-Survey).