Protein-protein interactions (PPIs) play key roles in a broad range of biological processes. Numerous strategies have been proposed for predicting PPIs, and among them, graph-based methods have demonstrated promising outcomes owing to the inherent graph structure of PPI networks. This paper reviews various graph-based methodologies, and discusses their applications in PPI prediction. We classify these approaches into two primary groups based on their model structures. The first category employs Graph Neural Networks (GNN) or Graph Convolutional Networks (GCN), while the second category utilizes Graph Attention Networks (GAT), Graph Auto-Encoders and Graph-BERT. We highlight the distinctive methodologies of each approach in managing the graph-structured data inherent in PPI networks and anticipate future research directions in this domain.