Due to its good corrosion resistance, stainless steel is widely used in many industrial fields. But in practical application, due to the joint action of corrosion environment and stress, pitting corrosion or cracks inevitably occur, thus leading to the decline of service performance, and even various safety accidents. Therefore, the corrosion behavior of stainless steel under stress has always been an important research topic in the field of stainless steel corrosion. In this paper, the research progress of localized corrosion behavior of some representative stainless steel materials under stress is summarized, and rules and causes of the influences of elastic stress, plastic stress and residual stress on pitting corrosion and corrosion cracking behavior are concluded. Till now, it is not particularly clear how elastic stress affects pitting corrosion and corrosion cracking of stainless steel. Generally, It is believed that elastic tensile stress will promote the initiation of pitting corrosion, which will lead to stress concentration in corrosion pits and promote corrosion propagation. However, it is also found that small elastic tensile stress can inhibit pitting corrosion, and its mechanism is not clear now. In addition, whether elastic compressive stress promotes or inhibits pitting corrosion initiation has yet to be agreed. The mechanism of the influence of the plastic stress on the localized corrosion of the stainless steel has been clarified. Plastic stress can lead to dislocation, thus promoting the pitting corrosion and crack growth. The residual tensile stress can promote the pitting corrosion and crack growth of stainless steel, but the residual compressive stress can effectively inhibit the pitting corrosion and crack growth. Therefore, the study on the localized corrosion behavior and its influence mechanism of stainless steel under low to medium elastic stress should be strengthened. For plastic stress and residual stress, characteristics of various stages and fracture impending characteristics of localized corrosion behavior of stainless steel should be further studied for the purpose of accurately assessing the risk of corrosion fracture and solving the problem of life assessment.