In this talk I will motivate the evaluation of nuclear reactions cross
sections from Lattice Quantum Chromodynamics (LQCD) and discuss
formalism recently developed for such calculations. In particular, I
will explore the connection between the energy spectrum of a three-
body system in a finite volume and infinite volume scattering matrix
elements using an effective field theoretical approach. The
implication of this formalism for studying systems composed of a
particle and a bound-state below the bound-state break-up will be
discussed. I will briefly discuss the similarities of the three-body
problem and that of two-body coupled-channels systems and discuss
challenges for studying scattering above the break-up threshold.