Generative artificial intelligence (GenAI) models have emerged as a transformative tool for addressing the complex challenges of drug discovery, enabling the design of structurally diverse, chemically valid, and functionally relevant molecules. Despite significant advancements, the rapid expansion of GenAI applications still faces challenges related to prediction accuracy, molecular validity, and optimization for drug-like properties. This review provides a comprehensive analysis of recent techniques and strategies aimed at enhancing the performance of GenAI models in molecular design. We explore key generative architectures, including variational autoencoders, generative adversarial networks, and transformer-based models, highlighting their unique contributions to drug discovery. Additionally, we discuss critical advancements such as reinforcement learning, multi-objective optimization, and the integration of domain-specific chemical knowledge, which collectively enhance molecular validity, novelty, and drug-likeness. Also, the review examines persistent challenges, including data quality limitations, model interpretability, and the need for improved objective functions, while offering insights into future research directions. By mapping the evolving landscape of GenAI-driven molecular design and providing strategic guidance for overcoming existing limitations, this review serves as an essential resource for researchers leveraging GenAI in drug discovery.