Large language models (LLMs) such as Generative Pre-trained Transformer 4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications including answering queries, code generation, and more. Parallelly, graph-structured data, intrinsic data types, are pervasive in real-world scenarios. Merging the capabilities of LLMs with graph-structured data has been a topic of keen interest. This article bifurcates such integrations into two predominant categories. The first leverages LLMs for graph learning, where LLMs can not only augment existing graph algorithms but also stand as prediction models for various graph tasks. Conversely, the second category underscores the pivotal role of graphs in advancing LLMs. Mirroring human cognition, we solve complex tasks by adopting graphs in either reasoning or collaboration. Integrating with such structures can significantly boost the performance of LLMs in various complicated tasks. We also discuss and propose open questions for integrating LLMs with graph-structured data for the future direction of the field.