The determination of the absolute configuration of a chiral compound of synthetic or natural origin is a problem that every organic chemist willl certainly have to face some day. An efficient and reliable method for the assignment of absolute stereostructures, independent of empirical CD rules, is the combination of experimental circular dichroism (CD) investigations with quantum chemical CD calculations. The availability of a broad variety of quantum chemical methods and the continuing appearance of new approaches permits - but also requires - the most appropriate method to be selected in each particular case, with respect to accuracy, time consumption, and computational resources. With examples of selected chiral compounds of the most diverse structures and origins, and inclusion of several methods based on substantially different theoretical backgrounds, this review describes the basic principles and concepts of quantum chemical CD calculations for the configurational assignment of chiral compounds with stereogenic centers and/or elements of axial or planar chirality. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)