The evolving field of generative artificial intelligence (GenAI), particularly generative deep learning, is revolutionizing a host of scientific and technological sectors. One of the pivotal innovations within this domain is the emergence of generative adversarial networks (GANs). These unique models have shown remarkable capabilities in crafting synthetic data, closely emulating real-world distributions. Notably, their application to gene expression data systems is a fascinating and rapidly growing focus area. Restrictions related to ethical and logistical issues often limit the size, diversity, and data-gathering speed of gene expression data. Herein lies the potential of GANs, as they are capable of producing synthetic gene expression data, offering a potential solution to these limitations. This review provides a thorough analysis of the most recent advancements at this innovative crossroads of GANs and gene expression data, specifically during the period from 2019 to 2023. In the context of the fast-paced progress in deep learning technologies, accurate and inclusive reviews of current practices are critical to guiding subsequent research efforts, sharing knowledge, and catalyzing continual growth in the discipline. This review, through highlighting recent studies and seminal works, serves as a key resource for academics and professionals alike, aiding their journey through the compelling confluence of GANs and gene expression data systems.