Abstract The methods of laser cooling of atoms have long been applied to obtain cold and ultracold atomic gases, including degenerate states and the atomic Bose–Einstein condensate in particular. Until recently the application of laser cooling methods to molecules was assumed to be impossible because of the complex structure of molecular levels and the absence of closed cooling cycles for transitions between the electron levels of molecules in the general case. However, it has recently become clear that laser cooling can be performed for a large class of molecules, including not only the simplest diatomic molecules but also polyatomic molecules. We here present the general principles for identifying suitable molecules and discuss current studies on and further developments in the laser cooling of molecules.