The derivation of an effective-mass Hamiltonian for studies of electron–hole pairs (multiexcitons) confined in semiconductor heterostructures such as quantum dots and quantum rings is presented. The obtained Schrödinger equation, describing the dynamics of the electrons and holes trapped in the quantum heterostructures, are solved at the Hartree-Fock self-consistent field, configuration interaction, and coupled-cluster levels. The computational methods, which are familiar from quantum chemical studies on molecules, have been generalized for simultaneously considering electrons and holes at the same level of theory. The methods and implementation of the ab initio computational methods including methods to calculate radiative recombination rates of multiexcitons and exciton relaxation rates due to phonon-multiexciton interaction are described. The applicability of the methods is demonstrated by studying multiexciton energies, photoluminescence spectra, and phonon relaxation rates of electrons trapped in quantum dots, quantum rings, and concentric quantum double rings. The calculations on the quantum dots and quantum rings show the importance of considering charge-carrier correlation effects in studies of energy levels and photoluminescence spectra, only the results obtained at highly correlated levels agree well with available experimental data. The calculations are also found to provide information about the dynamics of the charge carriers confined in the quantum heterostructures that supports novel interpretations of the photoluminescence experiments.