The definition of accurate stress-strain models, as well as guidance for how to select the appropriate model, is crucial for predicting material behaviour and aiding advanced structural analysis and design. To date, various stress-strain models have been developed for hot-rolled normal and high strength steels. This paper explores the existing models and establishes new unified models suitable across the full range of strength classes. Additionally, factors influ-encing the occurrence of a yield plateau are discussed and a simple criterion to distinguish between steels with a sharply-defined yield point and yield plat-eau and those with a rounded stress-strain response is proposed. Building on previous research, this study compiles the most comprehensive database to date, comprising over 1248 experimentally derived stress-strain curves on hot-rolled steel material collected from the global literature, encompassing a variety of steel grades, thicknesses and cross-section types. This paper analyses existing predictive expressions for the key material parameters based on the wider dataset collected and proposes some modifications where necessary. Overall, the proposed models enhance the understanding 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.