  This review focuses on the studies and computations of few-body systems of
electrons and holes in condensed matter physics. We analyze and illustrate the
application of a variety of methods for description of two- three- and
four-body excitonic complexes such as an exciton, trion and biexciton in
three-, two- and one-dimensional configuration spaces in various types of
materials. We discuss and analyze the contributions made over the years to
understanding how the reduction of dimensionality affects the binding energy of
excitons, trions and biexcitons in bulk and low dimensional semiconductors and
address the challenges that still remain.
