  Due to their intuitiveness, flexibility and relative numerical efficiency,
the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical
and semi-phenomenological model to describe optical propagation and coherent
light-matter interaction in media consisting of discrete-level quantum systems.
This review focuses on the application of this model to advanced optoelectronic
devices, such as quantum cascade and quantum dot lasers. The Bloch equations
are here treated as a density matrix model for driven quantum systems with two
or multiple discrete energy levels, where dissipation is included by Lindblad
terms. Furthermore, the one-dimensional MB equations for semiconductor
waveguide structures and optical fibers are rigorously derived. Special
analytical solutions and suitable numerical methods are presented. Due to the
importance of the MB equations in computational electrodynamics, an emphasis is
placed on the comparison of different numerical schemes, both with and without
the rotating wave approximation. The implementation of additional effects which
can become relevant in semiconductor structures, such as spatial hole burning,
inhomogeneous broadening and local-field corrections, is discussed. Finally,
links to microscopic models and suitable extensions of the Lindblad formalism
are briefly addressed.
