In this paper we discuss current challenges to the sustainability concept. This article focuses on seven dimensions of the concept. These dimensions are crucial for understanding sustainability. Even today, the literature contains basic misunderstandings about these seven dimensions. This article sketches such fallacies in the context of global and planetary sustainability. The sustainability concept has been criticized as a content-empty ‘fuzzy notion’ or non-committal ‘all-purpose glue’. This article thus has a critical intention of reflecting the sustainability concept accurately. The aim is to contribute a better understanding of the concept.