The coupled-cluster method has become one of the most widely used schemes for high-accuracy calculation of atomic and molecular energies and other properties. The two attributes which make the method so useful are its size extensivity (meaning that the energy of a system consisting of several non-interacting subsystems will be equal to the sum of subsystem energies) and the fact that truncation at, say, the double excitation term will bring in all powers and products of single and double excitations. These features turn out to be important in electronic structure calculationns, and are not shared by some of the other methods used in the field (e.g.\ configuration interaction).

The most widely used CCM is the single-reference method, applicable when the state of interest may be described approximately by a single Slater determinant. This method is now used routinely, and is incorporated in some of the widely distributed computational chemistry packages. The multireference case is more problematic. A variety of approaches has been tried and many successful applications reported, but no method applicable to all cases of multireference situations has emerged.

Many examples of applying the different CC methods will be given, to demonstrate the quality of results one may expect. The examples will include small and medium-size molecules as well as heavy and superheavy atoms, where CCM is applied in the frame of a relativistic many-body Hamiltonian.