  A review of coherent phenomena in photoexcited semiconductors is presented.
In particular, two classes of phenomena are considered: On the one hand the
role played by optically-induced phase coherence in the ultrafast spectroscopy
of semiconductors; On the other hand the Coulomb-induced effects on the
coherent optical response of low-dimensional structures.
  All the phenomena discussed in the paper are analyzed in terms of a
theoretical framework based on the density-matrix formalism. Due to its
generality, this quantum-kinetic approach allows a realistic description of
coherent as well as incoherent, i.e. phase-breaking, processes, thus providing
quantitative information on the coupled ---coherent vs. incoherent--- carrier
dynamics in photoexcited semiconductors.
  The primary goal of the paper is to discuss the concept of quantum-mechanical
phase coherence as well as its relevance and implications on semiconductor
physics and technology. In particular, we will discuss the dominant role played
by optically induced phase coherence on the process of carrier photogeneration
and relaxation in bulk systems. We will then review typical field-induced
coherent phenomena in semiconductor superlattices such as Bloch oscillations
and Wannier-Stark localization. Finally, we will discuss the dominant role
played by Coulomb correlation on the linear and non-linear optical spectra of
realistic quantum-wire structures.
