The work of this PhD investigates spontaneous collapse models, which are a proposed modification of quantum mechanics and their consistency with special relativity. Since soon after they were first proposed there have been many attempts to construct a relativistic collapse model, but currently there is not a satisfactory model. This thesis considers what it means for an irreversible dynamics to be consistent with special relativity and reviews the existing proposals and their issues. The key results are a demonstration of why a relativistic point-like collapse model is not possible and that a relativistic generalisation of one of the most studied collapse models, Continuous Spontaneous Localisation is not possible.
