This chapter explores deep learning methods for network analysis, focusing on graph neural networks (GNNs) and diffusion-based approaches. We introduce GNNs through a drug discovery case study, demonstrating how molecular structures can be analyzed as networks. The chapter covers GNN architecture, training processes, and their ability to learn complex network representations without explicit feature engineering. We then examine diffusion-based methods, which use random walks to develop network embeddings. These techniques are compared and contrasted with earlier spectral approaches, highlighting their capacity to capture nonlinear relationships and local network structures. Practical implementations using frameworks such as PyTorch Geometric illustrate the application of these methods to large-scale network datasets, showcasing their power in addressing complex network problems across various domains.