The closed-shell coupled cluster theory restricted to single and double excitation operators (CCSD) is formulated in a basis of nonorthogonal local correlation functions. Excitations are made from localized molecular orbitals into subspaces (domains) of the local basis, which strongly reduces the number of amplitudes to be optimized. Furthermore, the correlation of distant electrons can be treated in a simplified way (e.g., by MP2) or entirely neglected. It is demonstrated for 20 molecules that the local correlation treatment recovers 98%-99% of the correlation energy obtained in the corresponding full CCSD calculation. Singles-doubles configuration interaction (CISD), quadratic configuration interaction (QCISD), and Moller-Plesset perturbation theory [MP2, MP3, MP4(SDQ)] are treated as special cases.