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 lowdimensional semiconductors and address the challenges that still remain.1 In the summer of 2016 at the EFB23 conference in Aarhus, Denmark, following the inaugural ceremony establishing the Faddeev Medal, I spoke with L. D. Faddeev and mentioned that I would like to nominate Vitaly Efimov for this distinguished award. A smile touched Faddeev's face and he said simply, "great choice". In 2018, Vitaly Efimov and Rudolf Grimm became joint recipients of the Faddeev Medal for the theoretical prediction and ground-breaking experimental confirmation of the Efimov effect.