The fundamentals of the design and operation of self-priming pumps, as indispensable equipment in industry, have been the focus of research in the field of fluid mechanics. This paper begins with a comprehensive background on self-priming pumps and gas-liquid two-phase flow, and it outlines recent advances in the field. Self-priming pumps within the gas-liquid two-phase flow state and the spatial and temporal evolution of the transient characteristics of self-priming pumps determine the self-priming pump self-absorption performance. Through mastery of the self-absorption mechanism, high-performance self-absorption pump products can be formed to provide theoretical support for the development of products. In current research, numerical simulation has become an important tool for analyzing and predicting the behavior of gas-liquid two-phase flow in self-priming pumps. This paper reviews existing numerical models of gas-liquid two-phase flow and categorizes them. Reviewing these models not only provides us with a comprehensive understanding of the existing research but also offers possible directions for future research. The complexity of gas–liquid interactions and their impact on pump performance is analyzed. Through these detailed discussions, we are able to identify the challenges in the simulation process and summarize what has been achieved. In order to further improve the accuracy and reliability of simulations, this paper introduces the latest simulation techniques and research methodologies, which provide new perspectives for a deeper understanding of gas-liquid two-phase flow. In addition, this paper investigates a variety of factors which affect the operating efficiency of self-priming pumps, including the design parameters, fluid properties, and operating conditions. Comprehensive consideration of these factors is crucial for optimizing pump performance. Finally, this paper summarizes the current research results and identifies the main findings and deficiencies. Based on this, the need to improve the accuracy of numerical simulations and to study the design parameters in depth to improve pump performance is emphasized.