Pitting and crevice corrosion are major forms of degradation that affects stainless steel in chloride containing solutions. From a practical point of view, they produce localised corrosion, difficult to detect and, in the case of crevice corrosion, difficult to avoid. The purpose of this paper is not to give a comprehensive review of the pitting and crevice corrosion mechanisms: fundamental work as well as applied research were and are still devoted to this topic and entire books are dedicated to it. However, some basic knowledge of the mechanisms of these corrosion processes may help in the selection, specification and use of stainless steels. In the present paper we will present the main features of the pitting and crevice corrosion processes. We then focus on initiation and propagation mechanisms. The effects of main parameters regarding the material (composition, microstructure (heterogeneities such as non metallic inclusions)), the surface condition (effect of pollutions, biofilm), and the solution (redox potential) are summarised and illustrated using examples coming from the literature or author's experience. The standardised test methods and usual experiments used to characterise pitting and crevice corrosion resistance are given. More specific experimental approaches to predict the long term pitting corrosion resistance of alloys are discussed, such as metastable pitting and repassivation potentials. In the case of crevice corrosion, the geometrical parameters (width and depth) are key factors and more and more refined models are developed in the literature to define critical conditions.