The dynamics of open quantum systems is of great interest for many fields in physics and chemistry. For systems strongly interacting with their environments the dynamics are inherently non-Markovian, which is notoriously difficult to study and simulate. In this thesis I implement in detail the Hierarchy of Pure States (HOPS) and the recently developed Hierarchy of Matrix Product States (HOMPS) methods, which can be used to simulate non-Markovian dynamics. I then benchmark both methods using the spin-boson model.