Ab initio wave function-based electronic structure methods can compute highly accurate properties of molecular species in vacuo, and are widely used in computational chemistry. Moreover, they are systematically improvable and do not require empirical parameters. However molecular crystals present great difficulties for such methods, despite being composed of individually tractable fragments - the periodicity and long-range intermolecular interactions make fully ab initio calculations very expensive and difficult to implement. This is a problem, as accurate evaluation of the energetics of molecular crystals is a requirement for crystal structure prediction, which can provide considerable insight and predictive power for applications including materials science and pharmaceutical development. The intractability of high-level electronic structure methods for molecular crystals leads to computational studies on these systems typically employing density functional theory (DFT) . However , DFT as a theory is not systematically improvable and depends on the empirically determined functional. For particularly extensive studies, even DFT is too costly and approximate force field methods are used , though they are even more sensitive to parametrisation. It is preferable to develop methods which apply accurate, correlated electronic structure methods to the interactions in molecular crystals, but avoid full computations on the entire system. In this thesis, we describe several approaches using correlated wave function theories and a fragment-based truncated many-body expansion. The aim is to accurately compute the energetics of molecular crystals while performing high-level calculations on systems no larger than a molecular dimer.