Currently, considerable efforts are being focused on the development of reusable rockets and smart rockets due to the heavy requirements of future next-generation aerospace transportation. Safety, low-launching cost, and repeatability are expected from liquid rocket for fulfilling the big dreams of space transportation, exploration, and travelling. Therefore, research on fault detection of the liquid rocket engines (LRE) is critical for satisfying the above claims. Therefore, a comprehensive survey on the research and development of fault diagnosis systems and methods for the liquid rocket engines is presented. First, development history of liquid rocket engine diagnostic systems is reviewed thoroughly. Then three broad headings of the fault detection approaches of liquid rocket engines are divided through the summary and analysis of the existing methods, including approaches using signal processing, model-driven approach, and approach using artificial intelligence (AI). Then the paper discusses the concrete algorithms according to the classification features of the algorithms. In the end, the future developments of the fault detection approaches are presented, which will mainly pay attention to the reusability and intelligence of the rockets.