Dimethyl sulfoxide (DMSO) represents a dipolar aprotic solvent which incorporates a strongly polar sulfoxide group and two hydrophobic methyl moieties. Owing to its beneficial properties including low toxicity and environmental compatibility, DMSO has been and still is widely used as a solvent in industry as well as research. Applications can be found in many different areas ranging from medicine and biotechnology to electrochemistry and laser physics. In practical systems, DMSO is usually accompanied by other substances with whom it interacts at molecular scale. These interactions include, for instance, hydrogen bonds and van der Waals forces and determine the microscopic dissolution properties as well as the macroscopic solution behavior. Moreover, such interactions exert influence on the molecular structures of the involved molecules. In turn, this means that analyzing the molecular structure by means of theoretical and experimental approaches can shed light on the nature of interactions and help to achieve better understanding of the phenomena observed. In this article we review the literature reporting DMSO hydrogen bonding interactions with cosolvent molecules. In this context, theoretical as well as experimental studies are considered and compared in order to get a clear picture of this important solvent. Special attention is paid to the DMSO/water system which is well known for exhibiting a strongly nonideal mixing behavior. In addition, mixtures of DMSO with alcohols and other organic solvents are discussed.