In petroleum and chemical industry as well as other industrial processes, the elbows of pipeline transportation system are very easy to be eroded by solid particles entrained in the pipe, which reduces the pressure capacity of pipeline and increases the safety risk of pipeline transportation as a result. Firstly, this paper describes and analyzes the rules of API RP 14 E and DNV erosion prediction models used widely in oil and gas industry. Then, it summarizes the theories and models of solid particles erosion in elbow mentioned by many experts and scholars at home and abroad, including the classic micro-cutting theory model, the deformation wear theory model, E/CRC erosion model with high applicability, and Oka erosion model. On this basis, different erosion theories and models are compared and analyzed, and the internal relations among them as well as their advantages and disadvantages are summarized and pointed out. In terms of engineering application, the common anti-erosion coatings and anti-erosion geometric structures in industry in recent years are systematically summarized. The anti-erosion coatings include metal anti-erosion coatings, non-metal anti-erosion coatings and composite anti-erosion coatings. And the anti-erosion geometric structures include vortex structures and various forms of bionic rib structures. At the end of this paper, the research direction of theories and models of solid particle erosion in elbow, the development prospect of nanometer anti-erosion coatings and bionics anti-erosion rib structures are prospected. This paper can provide reference for the study of integrity management of oil and gas pipeline system, storage and transportation safety and flow guarantee of oil and gas.