Equivariant graph neural networks (EGNNs) have revolutionized molecular property prediction by encoding 3D structures while preserving physical symmetry. However, existing EGNNs struggle to capture fine-grained geometric features needed for tasks like understanding protein interactions, and designing molecules that modulate them are central challenges in computational drug discovery. This thesis develops a progressive framework based on equivariant graph neural networks (EqGNNs) that respects the geometric symmetries of molecular structures. Our contributions progress along two axes: from discriminative to generative and from basic representations to physics-informed, language-conditioned generation. In this study, we propose novel methods for both discriminative (E(Q)AGNN-PPIS, GDEGAN) and generative tasks (PhysFlow). Together, these advance symmetry-aware geometric deep learning for drug discovery.