In the contemporary era of technological advancements, integrating Generative Artificial Intelligence (AI) with radar systems has emerged as a groundbreaking approach to enhance the quality and clarity of radar data. This fusion has paved the way for significant improvements in data accuracy and interpretation and, expanded the potential applications of radar technology across various industries; including defense, meteorology, aviation, and autonomous vehicles. Generative AI algorithms, through their ability to learn from vast datasets and generate high-resolution radar imagery, have revolutionized how radar data is processed and analyzed. This paper provides a comprehensive survey of the current state-of-the-art Generative AI technologies applied to radar systems, highlighting critical methodologies, such as deep learning models and neural networks, that have been instrumental in achieving these advancements. Furthermore, it explores the challenges faced in the integration process, including data privacy concerns, computational demands, and the need for robust models capable of handling real-world variability. Through a detailed analysis of recent case studies and experimental results, this survey underscores the transformative impact of generative AI on enhancing radar data quality and clarity, thereby offering insights into future directions and potential breakthroughs in the field.