The structural design of concrete structures has to result in qualities ensuring ordinary structural safety and serviceability, together with durability. Recently, it has become necessary to pursue sustainability as well, and rather newly the issue of resilience has also appeared. It is now apparent that the effects of mechanical load, environmental load and even social coherence need to be reflected and included in the formulation of limit states. This is a complex matter involving the factors of time, service life, degradation effects, modelling, probability analyses, limit states, costs and other phenomena. It has not yet been completely understood, albeit several notions in this context are contained in different codes and regulations, e.g. EN 1990, EN 1992, ISO 13823:2008, ISO 16204:2012, fib MC2010 and fib MC2020 (currently under preparation by the fib committees). According to fib Model Code 2010, the design method most commonly used for concrete structures today is performance-based. Sustainable target value design can be briefly expressed as the comparison of sustainable capacity vs. sustainable impacts. This requires the formulation of a new class of limit states – apart from those of the engineering (or structural) type, also sustainability limit states now need to be specified. The presented contribution briefly mentions traditional and durability limit states, discussing their variants and context, and then concentrates specifically on the formulation of limit states for concrete sustainability at material level. It also presents some examples which apply a full probabilistic approach.