Quantitative structure-activity relationships (QSAR) are often employed to establish a correlation between structural features of potential drug candidates and their binding affinity towards a macromolecular target. In 3D-QSAR, the structures of the involved molecules are represented by three-dimensional entities, allowing to quantify electrostatic forces, hydrogen bonds and hydrophobic interactions at the atomic level. Models based on 3D-QSAR typically represent a binding site surrogate with physico-chemical properties mapped onto its surface or a grid surrounding the ligand molecules, superimposed in 3D space. Unfortunately such a single construct interacts with all ligands simultaneously, thus disabling the simulation of induced fit (receptor-to-ligand adaptation) - a fundamental shortcoming of the technology. As this entity represents all but a receptor surrogate, the bioactive conformation, orientation and protonation state of the ligand molecules might be guessed at best. Multidimensional QSAR represents a subtle extension of 3D-QSAR attempting to overcome both shortcomings. In this account, we review different concepts and demonstrate their use to predict binding affinities of chemically diverse sets of ligand molecules binding to G-protein coupled and nuclear receptors. By employing multi-dimensional QSAR on partially diverse and large data sets, predicitive r2 of 0.837 (neurokinin-1), 0.859 (bradykinin B2 receptor) and 0.907 (estrogen receptor) were for example obtained using the Raptor and Quasar software.