With the massive proliferation of data-driven algorithms, such as deep learning-based approaches, the availability of high-quality data is of great interest. Volumetric data is very important in medicine, as it ranges from disease diagnoses to therapy monitoring. When the dataset is sufficient, models can be trained to help doctors with these tasks. Unfortunately, there are scenarios where large amounts of data is unavailable. For example, rare diseases and privacy issues can lead to restricted data availability. In non-medical fields, the high cost of obtaining enough high-quality data can also be a concern. A solution to these problems can be the generation of realistic synthetic data using Generative Adversarial Networks (GANs). The existence of these mechanisms is a good asset, especially in healthcare, as the data must be of good quality, realistic, and without privacy issues. Therefore, most of the publications on volumetric GANs are within the medical domain. In this review, we provide a summary of works that generate realistic volumetric synthetic data using GANs. We therefore outline GAN-based methods in these areas with common architectures, loss functions and evaluation metrics, including their advantages and disadvantages. We present a novel taxonomy, evaluations, challenges, and research opportunities to provide a holistic overview of the current state of volumetric GANs.