  The vast majority of hadrons observed in nature are not stable under the
strong interaction, rather they are resonances whose existence is deduced from
enhancements in the energy dependence of scattering amplitudes. The study of
hadron resonances offers a window into the workings of quantum chromodynamics
(QCD) in the low-energy non-perturbative region, and in addition, many probes
of the limits of the electroweak sector of the Standard Model consider
processes which feature hadron resonances. From a theoretical standpoint, this
is a challenging field: the same dynamics that binds quarks and gluons into
hadron resonances also controls their decay into lighter hadrons, so a complete
approach to QCD is required. Presently, lattice QCD is the only available tool
that provides the required non-perturbative evaluation of hadron observables.
In this article, we review progress in the study of few-hadron reactions in
which resonances and bound-states appear using lattice QCD techniques. We
describe the leading approach which takes advantage of the periodic finite
spatial volume used in lattice QCD calculations to extract scattering
amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain
how from explicit lattice QCD calculations, one can rigorously garner
information about a variety of resonance properties, including their masses,
widths, decay couplings, and form factors. The challenges which currently limit
the field are discussed along with the steps being taken to resolve them.
