Unimers of both natural and synthetic origin self-assemble into liner, helical, columnar, planar and three-dimensional structures depending upon the functionality of supramolecular interactions. Recent reports describing the mechanism of formation, properties and possible applications of these systems are critically reviewed. The assembling of one-dimensional systems produces equilibrium polymers showing a length distribution and a degree of polymerization that may far exceed that of typical condensation polymers. Their growth may occur by a step-by-step process akin to polycondensation, and by cooperative processes such as helical growth or growth coupled to liquid crystallinity. Of particular interest are functional systems based on the coupling of a chemical reaction to supramolecular polymerization, and systems based on a covalent polymer hosted within the cavity of a supramolecular one. The assembly of two and three-dimensional systems occurs through a process akin to crystalization. The supramolecular organization of amphiphiles such as block copolymers is currently well described by the mean-field theory of unstable modes in homogeneous melts. An alternative, less sophisticated approach considers the growth of specifically designed building blocks. Possible applications are in the areas that expand the uses of covalent polymers, electrochemical and photonic devices, ion-selective channels, separation processes, microengines mimicking the performance of biological systems, storage of sequential information, biocompatible and patterned surfaces, sensors. A classification including additional systems that have been described as supramolecular polymers is presented.