Model-based approaches are becoming increasingly popular in the field of offline reinforcement learning, with high potential in real-world applications due to the model's capability of thoroughly utilizing the large historical datasets available with supervised learning techniques. This paper presents a literature review of recent work in offline model-based reinforcement learning, a field that utilizes model-based approaches in offline reinforcement learning. The survey provides a brief overview of the concepts and recent developments in both offline reinforcement learning and model-based reinforcement learning, and discuss the intersection of the two fields. We then presents key relevant papers in the field of offline model-based reinforcement learning and discuss their methods, particularly their approaches in solving the issue of distributional shift, the main problem faced by all current offline model-based reinforcement learning methods. We further discuss key challenges faced by the field, and suggest possible directions for future work.