The present state of research on multiexciton-impurity complexes is reviewed. These complexes are weakly bound nonequilibrium states of a shallow neutral impurity (a donor or acceptor) and several excitons in a semiconductor. Bound multiexciton complexes are stable because of the high degree of degeneracy of the bands of the semiconductor. The shell model for a multiexciton-impurity complex is discussed. According to this model, the electrons and holes in the complex fill shells successively in accordance with the Pauli principle. The shell model classifies the electron (or hole) states of the complex, with allowance for the local symmetry of the impurity center, and it predicts the number of lines in the spectra and their fine structure. The effects of the valley-orbit interaction and the crystal splitting on the fine structure in the spectrum are analyzed. The use of external agents (uniaxial deformations and magnetic fields) as tools for studying the internal structure of multiexciton-impurity complexes is discussed. Particular emphasis is placed on silicon, which has received the most experimental study.