This review focuses on the exfoliation of transition metal dichalcogenides MQ2 (TMD, M = Mo, W, etc., Q = S, Se, Te) in liquid media, leading to the formation of 2D nanosheets dispersed in colloids. Nowadays, colloidal dispersions of MoS2, MoSe2, WS2 and other related materials are considered for a wide range of applications, including electronic and optoelectronic devices, energy storage and conversion, sensors for gases, catalysts and catalyst supports, biomedicine, etc. We address various methods developed so far for transferring these materials from bulk to nanoscale thickness, and discuss their stabilization and factors influencing it. Long-time known exfoliation through Li intercalation has received renewed attention in recent years, and is recognized as a method yielding highest dispersed concentrations of single-layer MoS2 and related materials. Latest trends in the intercalation/exfoliation approach include electrochemical lithium intercalation, experimenting with various intercalating agents, multi-step intercalation, etc. On the other hand, direct sonication in solvents is a much simpler technique that allows one to avoid dangerous reagents, long reaction times and purifying steps. The influence of the solvent characteristics on the colloid formation was closely investigated in numerous recent studies. Moreover, it is being recognized that, besides solvent properties, sonication parameters and solvent transformations may affect the process in a crucial way. The latest data on the interaction of MoS2 with solvents evidence that not only solution thermodynamics should be employed to understand the formation and stabilization of such colloids, but also general and organic chemistry. It appears that due to the sonolysis of the solvents and cutting of the MoS2 layers in various directions, the reactive edges of the colloidal nanosheets may bear various functionalities, which participate in their stabilization in the colloidal state. In most cases, direct exfoliation of MQ2 into colloidal nanosheets is conducted in organic solvents, while a small amount of works report low-concentrated colloids in pure water. To improve the dispersion abilities of transition metal dichalcogenides in water, various stabilizers are often introduced into the reaction media, and their interactions with nanosheets play an important role in the stabilization of the dispersions. Surfactants, polymers and biomolecules usually interact with transition metal dichalcogenide nanosheets through non-covalent mechanisms, similarly to the cases of graphene and carbon nanotubes. Finally, we survey covalent chemical modification of colloidal MQ2 nanosheets, a special and different approach, consisting in the functionalization of MQ2 surfaces with help of thiol chemistry, interaction with electrophiles, or formation of inorganic coordination complexes. The intentional design of surface chemistry of the nanosheets is a very promising way to control their solubility, compatibility with other moieties and incorporation into hybrid structures. Although the scope of the present review is limited to transition metal dichalcogenides, the dispersion in colloids of other chalcogenides (such as NbS3, VS4, Mo2S3, etc.) in many ways follows similar trends. We conclude the review by discussing current challenges in the area of exfoliation of MoS2 and its related materials.