For a realistic description of optical processes in solid materials, it is essential to go beyond the simple picture of the optical Bloch equations and to treat many-body interactions that describe the coupling among the elementary material excitations by, e.g., the see article Coulomb interaction between the electrons and the coupling to other degrees of freedom, such as lattice vibrations, i.e., the electron-phonon coupling.
Within a semiclassical approach, where the light field is treated as a classical electromagnetic field and the material excitations are described quantum mechanically, all above mentioned effects can be treated microscopically on the basis of a many-body quantum theory.
For semiconductors the resulting system of equations are known as the semiconductor Bloch equations.
For the simplest case of a two-band model of a semiconductor, the SBEs can be written schematically as
Here  is the microscopic polarization and  and  are the electron occupations in the conduction and valence bands ( and ), respectively, and  denotes the crystal momentum.
As a result of the many-body Coulomb interaction and possibly further interaction processes, the transition energy  and the Rabi energy  both depend on the state of the excited system, i.e., they are functions of the time-dependent polarizations  and occupations  and , respectively, at all crystal momenta .
Due to this coupling among the excitations for all values of the crystal momentum , the optical excitations in semiconductor cannot be described on the level of isolated optical transitions but have to be treated as an interacting many-body quantum system.
A prominent and important result of the Coulomb interaction among the photoexcitations
is the appearance of strongly absorbing discrete excitonic resonances which show up in the absorption spectra of semiconductors spectrally below the fundamental band gap frequency. 
Since an exciton consists of a negatively charged conduction band electron and a positively charged valence band hole (i.e., an electron missing in the valence band) which attract each other via the Coulomb interaction, excitons have a hydrogenic series of discrete absorption lines. 
Due to the optical selection rules of typical III-V semiconductors such as Galliumarsenide (GaAs) only the s-states, i.e., 1s, 2s, etc., can be optically excited and detected, see article on Wannier equation.
The many-body Coulomb interaction leads to significant complications since it results in an infinite hierarchy of dynamic equations for the microscopic correlation functions that describe the nonlinear optical response.
The terms given explicitly in the SBEs above arise from a treatment of the Coulomb interaction in the time-dependent Hartree–Fock approximation. 
Whereas this level is sufficient to describe excitonic resonances, there are several further effects, e.g., excitation-induced dephasing, contributions from higher-order correlations like excitonic populations and biexcitonic resonances, which require one to treat so-called many-body correlation effects that are by definition beyond the Hartree–Fock level.
These contributions are formally included in the SBEs given above in the terms denoted by .
The systematic truncation of the many-body hierarchy and the development and the analysis of controlled approximations schemes is an important topic in the microscopic theory of the optical processes in condensed matter systems.
Depending on the particular system and the excitation conditions several approximations schemes have been developed and applied.
For highly excited systems, it is often sufficient to describe many-body Coulomb correlations using the second order Born approximation.
Such calculations were, in particular, able to successfully describe the spectra of semiconductor lasers, see article on semiconductor laser theory.
In the limit of weak light intensities, signature of exciton complexes, in particular, biexcitons, in the coherent nonlinear response have been analyzed using the dynamics controlled truncation scheme.
These two approaches and several other approximation schemes can be viewed as special cases of the so-called cluster expansion in which the nonlinear optical response is classified by correlation functions which explicitly take into account interactions between a certain maximum number of particles and factorize larger correlation functions into products of lower order ones.