The review addresses the structural and chemical features of 2D nanocrystals of metal oxide and hydroxides in the form of nanosheets (nanoflakes), basic methods for their synthesis and their applications. Nanocrystals with this type of morphology are characterized by high anisotropy of properties, exceptionally high proportion of surface atoms capable of interacting with the environment, relatively large number of defects in the structure, and a special quantum confined electronic subsystem. Nanosheets can be functionalized with various low-molecular-weight reagents. These features account for the unique physicochemical properties of metal oxide and hydroxide nanosheets and largely determine their practical significance. Consideration of issues of the preparative chemistry of these nanocrystals is focused on soft chemistry methods using solutions of metal salts, in particular chemical precipitation (including methods using templates), successive ionic layer deposition and reactions on the surface of bulk metals and at the solution/gas interface. Special attention is paid to the conditions of synthesis of nanosheet arrays, a sort of packages of single particles arranged in an ordered fashion on the substrate and oriented relative to the substrate. The applications of metal oxide and hydroxide nanosheets are considered. It is demonstrated that they are of considerable interest for applications in biomedicine, electrochemical energy engineering, chemical sensorics and photo- and electrocatalysis as parts of various functional nanomaterials with a unique set of physicochemical properties, including magnetic, electrophysical, electrochemical, optical, sorption and other properties. The bibliography includes 317 references