Within the Standard Model of particle physics, Quantum Chromodynamics (QCD) describes the strong interaction between particles carrying color charge. Lattice QCD provides a regularization of QCD by a grid in four-dimensional Euclidean space time. This regularization enables an ab-initio calculation of strong interaction properties in the non-perturbative regime. In this thesis, we will use lattice QCD to calculate properties of hadrons, the QCD bound states of quarks and gluons. While the calculation of ground state hadron masses is now routinely performed, lattice calculations of excited state properties are more difficult. In Euclidean correlation functions, which are measured on thelattice, contributions from excited states appear as sub-leading exponentials. This necessitates more elaborate methods to reliably extract such states. The isolation of these small contributions is the topicof this thesis. Our method of choice is the variational method and we will apply this method to several systems of interest.