Generative Artificial Intelligence (GAI) represents an emerging field that promises the creation of synthetic data and outputs in different modalities. GAI has recently shown impressive results across a large spectrum of applications ranging from biology, medicine, education, legislation, computer science, and finance. As one strives for enhanced safety, efficiency, and sustainability, generative AI indeed emerges as a key differentiator and promises a paradigm shift in the field. This article explores the potential applications of generative AI and large language models in geoscience. The recent developments in the field of machine learning and deep learning have enabled the generative model's utility for tackling diverse prediction problems, simulation, and multi‐criteria decision‐making challenges related to geoscience and Earth system dynamics. This survey discusses several GAI models that have been used in geoscience comprising generative adversarial networks (GANs), physics‐informed neural networks (PINNs), and generative pre‐trained transformer (GPT)‐based structures. These tools have helped the geoscience community in several applications, including (but not limited to) data generation/augmentation, super‐resolution, panchromatic sharpening, haze removal, restoration, and land surface changing. Some challenges still remain, such as ensuring physical interpretation, nefarious use cases, and trustworthiness. Beyond that, GAI models show promises to the geoscience community, especially with the support to climate change, urban science, atmospheric science, marine science, and planetary science through their extraordinary ability to data‐driven modelling and uncertainty quantification.