Generative Artificial Intelligence (Generative AI) has rapidly evolved as one of the most influential paradigms in modern computing, enabling machines to generate new and meaningful content such as text, images, audio, video, and synthetic data. The recent emergence of deep generative models, including Generative Adversarial Networks, Variational Autoencoders, Diffusion Models, and Transformer-based Large Language Models, has significantly expanded the applicability of artificial intelligence across diverse domains. This paper presents a systematic review of Generative AI models, focusing on their theoretical foundations, architectural advancements, and real-world applications in healthcare, education, finance, cybersecurity, creative industries, and intelligent systems. The review also examines key challenges such as ethical concerns, bias, explainability, privacy, and computational cost. Finally, the paper identifies open research gaps and future directions to support the responsible and sustainable development of Generative AI technologies.