Geomodelling of subsurface reservoirs is of great significance to the development of hydrocarbon and water resources as well as carbon capture and storage (CCS). Traditional geostatistics-based geomodelling approaches (e.g., variogram- or multiple point statistics-based) produce geomodels that are to some extent consistent with geological patterns but have apparent flaws when the patterns become complicated. Generative Adversarial Networks (GANs) in deep learning can abstract and reproduce complicated spatial patterns and have been used successfully in many areas. In recent years, GANs have been combined with geomodelling, where the generator composed of Convolutional Neural Networks (CNN) can first learn complicated geological patterns and then produce realistic reservoir geomodels. The GANs-based geomodelling approach has been researched and improved in many aspects. Researchers have even applied this method in the 3D geomodelling of complicated field reservoirs, much of which has achieved excellent performance. This paper reviews the research progress of the GANs-based geomodelling approach. The unconditional geomodelling approach can be classified into two categories, namely conventional and progressive GANs-based methods, based on the training manner of GANs. With a conventional manner, all CNN layers of the generator and discriminator are concurrently trained, while with a progressive manner, they are trained layer by layer from shallow to deep. The progressive manner allows the generator to learn geological patterns from coarse to fine scales and thus is superior to the conventional alternative in terms of the output quality and training time. To produce geomodels that are consistent with not only expected geological patterns but also the given conditioning data, GANs-based conditional geomodelling approaches are proposed. One of the conditional approaches is the post-GANs latent vector searching method, where proper input latent vectors of a pretrained generator are searched using the gradient descent or the Markov Chain Monte Carlo (MCMC) methods. In this context, geomodels consistent with given conditioning data can be produced from these proper latent vectors by the pretrained generator. However, once the given conditioning data change, another set of proper latent vectors needs to be searched, which requires a lot of time and computational resources. As a countermeasure, the direct conditional simulation method based on GANs (GANSim) is proposed. In GANSim, the generator is trained to learn both geological patterns and relationships between various conditioning data and the geomodel; with these two types of learned knowledge, the generator can directly map any given conditioning data into geomodels that are consistent with both geological patterns and conditioning data. GANSim is expanded into 3D to form a GANSim-3D framework, which has been successfully applied in 3D geomodelling of karst cave reservoirs in the Tahe Oilfield. Finally, several prospects are proposed as potential future working directions, involving GANSim frameworks, training resources, industrialization potentials, and digitalization of geologic knowledge.