The paper first reviews different interpretations of robustness. On this basis objectives facilitating the quantification of robustness of engineering systems are formulated. Thereafter a generic framework for risk assessments of engineering systems is presented in which robustness is related to the ability of the system to sustain damages. This framework is then applied to quantify robustness of structural systems and to develop a robustness index facilitating a consistent ranking of structures according to their robustness. The proposed approach to the assessment of robustness principally takes into account the effect of redundancy, ductility, damage and failure consequences as well as strategies for condition control and intervention during the service life of structures. Finally, a simple example illustrates the use of the framework for the assessment of the robustness of a jacket steel structure subject to fatigue damage. The example shows that presently used indicators for the robustness of jacket type steel structures such as the RIF only capture part of the picture and illustrates the merits of a risk based framework for robustness assessments.