In recent years, deep learning based generative models, particularly Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and Diffusion Models (DMs), have been instrumental in in generating diverse, high-quality content across various domains, such as image and video synthesis. This capability has led to widespread adoption of these models and has captured strong public interest. As they continue to advance at a rapid pace, the growing volume of research, expanding application areas, and unresolved technical challenges make it increasingly difficult to stay current. To address this need, this survey introduces a comprehensive taxonomy that organizes the literature and provides a cohesive framework for understanding the development of GANs, VAEs, and DMs, including their many variants and combined approaches. We highlight key innovations that have improved the quality, diversity, and controllability of generated outputs, reflecting the expanding potential of generative artificial intelligence. In addition to summarizing technical progress, we examine rising ethical concerns, including the risks of misuse and the broader societal impact of synthetic media. Finally, we outline persistent challenges and propose future research directions, offering a structured and forward looking perspective for researchers in this fast evolving field.