Generative Artificial Intelligence (AI) has significantly impacted drug discovery in recent years by reducing costs and enhancing de novo drug design capabilities. The complexity of drug design, due to the vast number of possible molecules, makes the process challenging. However, advancements in hardware and the remarkable results from deep learning methods and generative models have revolutionized the pharmaceutical industry by leveraging cutting-edge technology. The three key challenges precision, cost reduction, and speeding up the drug design process can be addressed using generative models and AI approaches. Various Generative AI(GenAI) methods, including generative adversarial networks (GANs), variational autoencoders (VAEs), diffusion models, flow-based models, and transformer-based models like large language models (LLMs), have all contributed significantly to recent advancements. Recurrent neural networks, including LSTM and GRU architectures, have been applied to sequence-based tasks in drug discovery, while reinforcement learning (RL) techniques have been employed to refine drug development strategies through feedback mechanisms. In this chapter, we introduce these GenAI models and explore their diverse applications in drug research.