This article provides a comprehensive overview of generative artificial intelligence (GenAI) by tracing its evolution from early techniques such as Gaussian mixture models (GMMs) to recent advances like generative adversarial networks (GANs) and transformer-based models. Additionally, it outlines various key generative frameworks like variational autoencoders (VAEs), deep belief networks (DBNs), deep Boltzmann machines (DBMs), and normalizing flows. Additionally, the article analyzes their respective strengths and weaknesses in modeling complex data distributions. Specifically, it discusses how GANs can produce highly realistic outputs but risk mode collapse, while VAEs impose useful structure but can over-smooth details.