  The problem of a few interacting fermions in quantum physics has sparked
intense interest, particularly in recent years owing to connections with the
behavior of superconductors, fermionic superfluids, and finite nuclei. This
review addresses recent developments in the theoretical description of four
fermions having finite-range interactions, stressing insights that have emerged
from a hyperspherical coordinate perspective. The subject is complicated, so we
have included many detailed formulas that will hopefully make these methods
accessible to others interested in using them. The universality regime, where
the dominant length scale in the problem is the two-body scattering length, is
particularly stressed, including its implications for the famous BCS-BEC
crossover problem Derivations and relevant formulas are also included for the
calculation of challenging few-body processes such as recombination.
