In this talk , we will overview a series of recent results on global well-posedness and scattering in the energy-supercritical range (dimensions five and higher) for the defocusing cubic nonlinear wave equation (NLW). More precisely, in a series of works, we prove global well-posedness under an a priori uniform in time control of the critical Sobolev norm by establishing strong integrability and regularity properties for a particular class of solutions to NLW.