Discovering novel pharmaceutical drugs is a lengthy, complex, and resource-intensive process. Traditional approaches in chemoinformatics have provided valuable tools for predicting molecular properties, but these methods can fall short in terms of efficiency and predictive accuracy. When used in molecular generation, these limitations become more pronounced, as inaccuracies in property prediction can lead to the design of suboptimal candidates. This dissertation explores innovative approaches to drug discovery through the application of deep graph representation learning techniques, focusing on two areas: molecular property prediction and molecular generation. We propose novel graph neural network architectures designed to enhance expressiveness in 2D and 3D molecular graphs. Our approach incorporates feature transformations inspired by hypercomplex algebras or integrates group equivariance into the models, facilitating data-efficient training. For 3D molecular data, we demonstrate that rotation-equivariant networks can be scaled to process larger biomolecules and outperform invariant networks while remaining computationally efficient. Additionally, we introduce generative models based on diffusion probabilistic models that sample new 3D molecular structures with targeted properties, either for ligands in isolation or within protein-ligand complexes, using rotation-equivariant graph networks as denoisers. This aspect of our research aims to enhance the drug discovery pipeline by improving the efficiency of identifying promising drug candidates that meet multiple criteria. The results of this thesis suggest that deep graph representation learning has the potential to advance drug discovery by providing more accurate predictive tools and enhancing the ability to generate novel molecular candidates. This work contributes to the development of computational methods in drug discovery and may pave the way for further research into applying graph representation learning to complex chemical problems.