Protein functions often involve a dynamic interplay that covers a variety of molecular interactions that can be represented and analyzed in a 3-dimensional space. To this end, researchers have applied graph neural networks (GNNs) that effectively model such spaces as a promising methodology to predict protein functions. We discuss the graph-based representations of proteins that are applied to different prediction tasks, which include graphs at various levels of granularity: atomic, residue, and multi-scale. We also review various protein function prediction tools that rely on GNN architectures that learn representations from protein graphs, specifically in the context of the Gene Ontology prediction and protein–protein interaction prediction. GNN-based methods leverage the underlying structural knowledge and offer a promising future in improving the quality of the protein function predictions.