The quark-gluon plasma (QGP) is conjectured to have existed in the early stages of the Big Bang and it has been discovered in heavy ion collisions. The internal properties of the medium are not well understood. Due to its large mass and long thermalisation time, the charm quark is an excellent tool with which to probe the plasma. In this thesis I study the dissociation of open and hidden charm mesons. Lattice QCD provides a non-perturbative means of studying the spectral quantities of charmed mesons. The suppression of J= in medium is widely considered to be a signal for deconfinement. I will use J= to study the heavy quark diffusion through the QGP. Jet-quenching observed in heavy ion collision experiments may be studied through the D mesons, increasing experimental interest in open charm. I will present the first study of the spectral functions of these mesons. The finite resolution in the time direction is one of the main limiting factors in obtaining reliable spectral functions from lattice QCD. In order to reduce the ensuing uncertainties we are currently producing a set of highly anisotropic lattices which will greatly improve the accuracy of our results. I will outline the method employed in the generation of these ensembles and present preliminary results.