Quantitative structure-activity relationships (QSAR) are an area of computational research which builds atomistic or virtual models to predict the biological activity or the toxicity of known or hypothetical substances. Of particular interest for the biomedical sciences are three-dimensional receptor surrogates (3D-QSAR) because they allow for the simulation of directional forces such as hydrogen bonds or metal-ligand contacts--key interactions for both molecular recognition and stereospecific ligand binding. While more powerful approaches make use of a genetic algorithm or a neural network to evolve a receptor surrogate, its predictive power still critically depends on the spatial alignment of the ligand molecules--mirroring the pharmacophore hypothesis--used to construct it. To avoid this bias, a recent development at our laboratory includes the possibility to represent each ligand molecule by an ensemble of conformations, orientations and protonation states as the fourth dimension (4D-QSAR). In addition, it allows for a potentially flexible receptor site (mimicking local induced fit) and solvent-accessible or shallow binding pockets. In this account, we seek to document the superiority of 4D-QSAR compared to 3D-concepts with simulations on the steroid, the aryl hydrocarbon and the neurokinin-1 receptor system. More complex, future applications of 4D-QSAR--the establishment of a virtual laboratory for the assessment of receptor-mediated toxicity and the prediction of oral bioavailability--are outlined.