  Few-body physics has played a prominent role in atomic, molecular and nuclear
physics since the early days of quantum mechanics. It is now possible---thanks
to tremendous progress in cooling, trapping, and manipulating ultracold
samples---to experimentally study few-body phenomena in trapped atomic and
molecular systems with unprecedented control. This review summarizes recent
studies of few-body phenomena in trapped atomic and molecular gases, with an
emphasis on small trapped systems. We start by introducing the free-space
scattering properties and then investigate what happens when two particles,
bosons or fermions, are placed in an external confinement. Next, various
three-body systems are treated analytically in limiting cases. Our current
understanding of larger two-component Fermi systems and Bose systems is
reviewed, and connections with the corresponding bulk systems are established.
Lastly, future prospects and challenges are discussed. Throughout this review,
commonalities with other systems such as nuclei or quantum dots are
highlighted.
