Generative adversarial networks (GANs) are one powerful type of deep learning models that have been successfully utilized in numerous fields. They belong to the broader family of generative methods, which learn to generate realistic data with a probabilistic model by learning distributions from real samples. In the clinical context, GANs have shown enhanced capabilities in capturing spatially complex, nonlinear, and potentially subtle disease effects compared to traditional generative methods. This review critically appraises the existing literature on the applications of GANs in imaging studies of various neurological conditions, including Alzheimer's disease, brain tumors, brain aging, and multiple sclerosis. We provide an intuitive explanation of various GAN methods for each application and further discuss the main challenges, open questions, and promising future directions of leveraging GANs in neuroimaging. We aim to bridge the gap between advanced deep learning methods and neurology research by highlighting how GANs can be leveraged to support clinical decision making and contribute to a better understanding of the structural and functional patterns of brain diseases.