The stress-strain characteristics of structural steels are predominantly influenced by their chemical composition, manufacturing process and heat treatment. To date, various stress-strain models have been developed for hot-rolled and cold-formed normal and high strength steels. This paper reviews the existing stress-strain models and establishes new unified models suitable for both normal and high strength steels (HSS). Additionally, factors influencing the occurrence and length of the yield plateau are discussed and a simple criterion to distinguish between steels with a sharply-defined yield point and yield plateau and those with a rounded stress-strain response is proposed. Building on previous research, a comprehensive database, comprising over 2850 experimentally derived stress-strain curves on hot-rolled and cold-formed steels from the global literature, has been compiled and analysed. These curves encompass a wide range of steel grades, with the coupon specimens extracted from various cross-section profiles. The accuracy of existing predictive expressions for the key material parameters is assessed and new predictive expressions are introduced where necessary. Overall, the proposed models enhance the consistency, range of applicability and predictive accuracy of stress-strain curves for structural steels, which are essential for facilitating the growing use of advanced computational methods in the analysis and design of steel structures.