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 EFTs 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.
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