Food web theory, which bridges community ecology and ecosystem ecology and unifies the research of biodiversity and ecosystem function, holds the key for understanding the operation mechanism of ecosystems. Since the famous debate on "complexity-stability" invoked by Robert May's classical work in 1973, researchers began to realize that stability is an important premise of food webs for their structure maintenance, function exertion and dynamic evolution. During the past half century, the exploration of food web stability has transitioned from qualitative food webs containing only topological relations to quantitative food webs that also containing interaction strength. A series of mechanisms such as self-limiting, weak interaction and adaptive predation have been proposed, and a "module-web" double-layer framework has been gradually established. Based on previous studies, we figured out the various stability mechanisms at the module level and the integration mechanisms of each module at the whole web level, which further enhanced this framework. To overcome its shortcomings in the face of complex food webs, we further proposed a food web stability framework based on a hierarchical structure. From the perspective of dynamics and energetics, the internal stability mechanism of each level and the relationship between the levels were discussed in order to provide some ideas for building a more universal food web stability theory. Future research directions include:(1) expanding the research on stability mechanism from food webs to more general ecological networks; (2) obtaining a deeper understanding of the structure and dynamics of food webs through comprehensively considering influencing factors such as biophysical elements, dynamic stability, the pursuit of energy flow power by the system, the stability of the environment, and evolution history.