A comprehensive classification of contrast agents currently used or under development for magnetic resonance imaging (MRI) is presented. Agents based on small chelates, macromolecular systems, iron oxides and other nanosystems, as well as responsive, chemical exchange saturation transfer (CEST) and hyperpolarization agents are covered in order to discuss the various possibilities of using MRI as a molecular imaging technique. The classification includes composition, magnetic properties, biodistribution and imaging applications. Chemical compositions of various classes of MRI contrast agents are tabulated, and their magnetic status including diamagnetic, paramagnetic and superparamagnetic are outlined. Classification according to biodistribution covers all types of MRI contrast agents including, among others, extracellular, blood pool, polymeric, particulate, responsive, oral, and organ specific (hepatobiliary, RES, lymph nodes, bone marrow and brain). Various targeting strategies of molecular, macromolecular and particulate carriers are also illustrated.