Graph neural networks extend deep learning to data that is naturally represented as graphs, such as molecules, social networks or transportation systems. Instead of operating on fixed grids like images, they work on nodes connected by edges, with both nodes and edges potentially carrying features.

Modern graph neural networks use message passing: each node aggregates information from its neighbors, updates its representation and repeats this over several layers. Variants differ in how they aggregate and transform information. Graph convolutional networks generalize convolution by averaging or summing neighbor features with learned weights. Graph attention networks use attention mechanisms so nodes weight neighbors differently, focusing on the most relevant connections. Other models incorporate edge features, directionality or hierarchical pooling.

These architectures support both supervised and self supervised learning. In supervised settings, they can predict properties of individual nodes, whole graphs or edges. Self supervised methods design pretext tasks such as predicting masked nodes or contrasting different views of the same graph, which improves performance with limited labels.

Applications span drug discovery, protein structure, chemistry, recommender systems, traffic prediction and fraud detection. In science and engineering, they capture complex relational structure in physical systems, materials and molecules, enabling more accurate and data efficient models.

Challenges include oversmoothing, where node representations become indistinguishable as depth increases, and oversquashing, where long range information is compressed through narrow bottlenecks. Recent work explores improved architectures, positional encodings, better expressivity relative to classical graph algorithms and scalable training on large graphs. Overall, graph neural networks provide a powerful and flexible framework for learning from relational data.