I introduce and define Quantum Chromodynamics. I describe various well-known nonperturbative techniques for calculating quantities from the theory and discuss their merits and deficiencies. I then motivate and define a non-relativistic formulation (NRQCD) of the theory. I discuss the mechanics of the extraction of numbers from numerical simulations, and present general arguments as to the expected form of these data. I present results and details of their extraction from simulations of heavy-heavy and heavy-light mesons using NRQCD. I compare these results with those from other calculations and with experimental data, where they exist. I make suggestions for further work. An appendix contains details of the code used in the simulation together with the input parameters of the simulation.