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Summary form only given. The nonlinear optical absorption in low dimensional semiconductors are well described by semiconductor Bloch equations, derived from Green's functions or projection techniques. Different versions of these equations have quite successfully described isolated quantum wells, coupled superlattices and bulk materials. A careful analysis within the frame of a recent many-body theory, considering in detail the interplay between Coulomb-Hartree-Fock and scattering contributions, shows e.g. that the density dependent shift of the excitonic peak depends on temperature for three-dimensional bulk samples, reproducing recent experimental findings. The question is at this moment open, on what a theory at that level, including non-diagonal dephasing and dynamical screening of the Coulomb interaction might predict as the system evolves from quasi-three to quasi-two dimensions.