In solids, the many-body wavefunction has an overwhelmingly complicated structure such that the direct wave-function-solution techniques are intractable. The cluster expansion is a variant of the coupled-clusters approach and it solves the dynamical equations of correlations instead of attempting to solve the quantum dynamics of an approximated wavefunction or density matrix. It is equally well suited to treat properties of many-body systems and quantum-optical correlations, which has made it very suitable approach for semiconductor quantum optics.