Abstract In 2003 the Belle collaboration announced the discovery of the X (3872) particle. This was confirmed shortly thereafter by the CDF, D0 and BaBar collaborations, and later by the LHCb collaboration. Based on the decay modes that have been observed to date, it is clear that this particle is a hadron, that is, a composite particle that experiences the strong nuclear force. The X (3872) was found within a family of well understood hadrons called charmonia. Interestingly, it is quite difficult to interpret the X (3872) as a charmonium state. For this reason it has been widely speculated that the X (3872) cannot be understood in terms of the quark model, unlike the vast majority of hadrons observed to date. Such hitherto unobserved particles are called exotic hadrons. Since the discovery of the X (3872), many similarly anomalous charmonium-like particles have been discovered. As would be expected, some unanticipated hadrons have also been found in the closely related bottomonium spectrum. These particles are collectively referred to as heavy quarkonium-like. Evidence is growing that at least some of these particles are exotic hadrons. If confirmed, this would have dramatic implications for our understanding of the strong nuclear force. A major experimental and theoretical effort is now underway in the field of hadron spec- troscopy to determine the identities of the heavy quarkonium-like states. In order to investi- gate the possibility that some of these states could be exotic hadrons, theoretical calculations are needed to firmly establish their properties. One of the main arguments for the existence of exotic hadrons is that they are predicted by the fundamental theory of the strong interac- tion, Quantum Chromodynamics (QCD). Therefore it is desirable to predict the properties of exotic hadrons using a theoretical approach that is firmly based in QCD. One such method is QCD sum rules (QSR). The research presented here uses the QSR technique to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third ii