Generative modeling has emerged as a powerful tool for molecular design and structure prediction, offering the ability for molecular discovery. However, challenges such as synthetic feasibility, novelty, diversity of generated molecules, and generalization ability of predictions remain critical for real-world applications, particularly in drug discovery. In this presentation, we introduce an overview of state-of-the-art generative models, including graph-based methods, generative flow networks, and diffusion methods, all aimed at addressing these challenges. First, we will show how generative modeling can facilitate the structural prediction of protein-ligand complexes and its expansion. Second, we focus on strategies that improve the synthesizability of generated molecules by incorporating chemical reaction templates, enabling the generation of novel compounds that are not only drug-like but also synthetically accessible. Third, large language models fine-tuned with drug-related data can be used to elucidating complex relationships between drugs, proteins, and diseases. Through case studies in drug design and broader molecular applications, we demonstrate how these generative modeling can help accelerate drug discovery, offering a pathway to more practical and innovative solutions across molecular discovery domains.