  Nuclear halos emerge as new degrees of freedom near the neutron and proton
driplines. They consist of a core and one or a few nucleons which spend most of
their time in the classically-forbidden region outside the range of the
interaction. Individual nucleons inside the core are thus unresolved in the
halo configuration, and the low-energy effective interactions are short-range
forces between the core and the valence nucleons. Similar phenomena occur in
clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some
exotic hadrons. In these weakly-bound quantum systems universal scaling laws
for s-wave binding emerge that are independent of the details of the
interaction. Effective field theory (EFT) exposes these correlations and
permits the calculation of non-universal corrections to them due to
short-distance effects, as well as the extension of these ideas to systems
involving the Coulomb interaction and/or binding in higher angular-momentum
channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo
nuclei, has been used to compute the properties of single-neutron, two-neutron,
and single-proton halos of s-wave and p-wave type. This review summarizes these
results for halo binding energies, radii, Coulomb dissociation, and radiative
capture, as well as the connection of these properties to scattering
parameters, thereby elucidating the universal correlations between all these
observables. We also discuss how Halo EFT's encoding of the long-distance
physics of halo nuclei can be used to check and extend ab initio calculations
that include detailed modeling of their short-distance dynamics.
