<p>Generative Artificial Intelligence (GenAI) has seen a remarkable growth in recent years, expanding beyond traditional discriminative tasks to the generation of new content, such as text, images, and videos, based on patterns discovered in the existing data. Advances in deep learning, particularly the development of novel architectures such as Transformers, Generative Adversarial Networks, Diffusion Models, and Variational Autoencoders have significantly contributed to this progress. GenAI has rapidly evolved, demonstrating advanced capabilities across a wide range of real-world applications such as healthcare, and creative industries. In this paper, we explore the current foundations of GenAI to provide a comprehensive overview of its principal models and their variants, highlighting their use cases, strengths, and limitations. This survey introduces an architecture-based structured taxonomy of GenAI models, laying the groundwork for the development of more efficient generative applications and encouraging further advancements within the field.</p>