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.