Concrete is undoubtedly the most important and widely used construction material of the last centuries. Nevertheless, mathematical models that can accurately capture the particular material behaviour under all loading conditions of significance are scarce at best. Although concepts and suitable models have existed for quite a while, their practical significance is low due to the limited attention to calibration and validation requirements and the scarcity of robust, transparent and comprehensive methods to perform such tasks. Therefore, the manuscript attempts to promote the use of advanced concrete constitutive models by thoroughly reviewing their differences regarding calibration and validation on a selected consistent experimental data set. More specifically, only two generally available standard experimental tests, i.e. a three-point bending test and a compression cube test, are employed. The quality of fits is objectively quantified using three independent measures based on the mean experimental curves.