Recent developments in first-principles lattice dynamics and classical force field based molecular dynamics are revolutionising the field of neutron spectroscopy. Herein we present a short review of these methods, their critical role in the supporting of cutting-edge experiments, and how they are improved by matching experimental data. We begin with a brief overview of how lattice dynamics calculations can be compared to inelastic neutron scattering (INS) and molecular dynamics simulations to both INS and quasi-elastic neutron scattering (QENS). We then provide a series of exemplar applications where lattice dynamics and molecular dynamics have been used in conjunction with neutron spectroscopy to bring significant understanding to topical areas of materials science namely: (i) lattice dynamics and INS for the study of hybrid organic-inorganic perovskites (ii) lattice dynamics and INS for the study of flexible porous solids and (iii) molecular dynamics and QENS for probing molecular behaviour in zeolite catalysis. In all three cases, the understanding gained through the synergy of experiment and computation would have been significantly reduced using either in isolation. Finally, we consider the current state of the art, describing outstanding challenges and suggesting future directions in this exciting and fertile area of physical science.