  Controlling light at the level of individual photons has led to advances in
fields ranging from quantum information and precision sensing to fundamental
tests of quantum mechanics. A central development that followed the advent of
single photon sources was the observation of the Hong-Ou- Mandel (HOM) effect,
a novel two-photon path interference phenomenon experienced by
indistinguishable photons. The effect is now a central technique in the field
of quantum optics, harnessed for a variety of applications such as diagnosing
single photon sources and creating probabilistic entanglement in linear quantum
computing. Recently, several distinct experiments using atomic sources have
realized the requisite control to observe and exploit Hong-Ou-Mandel
interference of atoms. This article provides a summary of this phenomenon and
discusses some of its implications for atomic systems. Transitioning from the
domain of photons to atoms opens new perspectives on fundamental concepts, such
as the classification of entanglement of identical particles. It aids in the
design of novel probes of quantities such as entanglement entropy by combining
well established tools of AMO physics - unity single-atom detection, tunable
interactions, and scalability - with the Hong-Ou-Mandel interference.
Furthermore, it is now possible for established protocols in the photon
community, such as measurement-induced entanglement, to be employed in atomic
experiments that possess deterministic single-particle production and
detection. Hence, the realization of the HOM effect with atoms represents a
productive union of central ideas in quantum control of atoms and photons.
