Representative applications of the coupled cluster method to atomic and molecular systems are described. Properties calculated for molecules include potential energy surfaces, geometries, ionization potentials and excitation energies. For atomic systems, emphasis is put on heavy atoms, where the relativistic coupled cluster scheme yields atomic transition energies with unprecedented accuracy. The nature of the ground state is investigated for some superheavy (Z>100) atoms; strong relativistic effects produce in many cases ground states different from those of lighter elements in the same group of the periodic table.