The thesis is situated in the domain of contemporary metaphysics of science. The question is which ontology fits best with our knowledge of the world. The method chosen is the one of evaluating the consequences of different ontological frameworks against the background of our scientific knowledge of the world. The thesis analyses the two main frameworks in today's metaphysics of science, Humeanism and dispositionalism. It advocates that only an unorthodox version of Humeanism and only an unorthodox version of dispositionalism can be defended, the unorthodox character of these versions consisting in taking the fundamental properties to be relations rather than intrinsic properties. The thesis then sets out in detail what such an unorthodox version of Humeanism amounts to. Chapters 1 and 2 introduce the standard versions of Humeanism and dispositionalism, focussing on the accounts of laws of nature and causation. Chapter 3 compares both these positions and concludes that as far as the orthodox versions are concerned, dispositionalism fares better than Humeanism, since it can avoid Humeanism's commitments to quidditism and humility. However, as is argued in chapter 4, instead of replying to the objections from quidditism and humility by switching to dispositionalism, there is an unorthodox version of Humeanism available that does not run into these problematic consequences and that is supported by science: if one takes the fundamental physical properties to be relations instead of intrinsic properties, the objection from quidditism is avoided, since there is no hidden intrinsic essence of relations. As regards the objection from humility, one can maintain that science is in principle able to provide knowledge of the fundamental relations that there are in the world so that there is no principled ignorance. Consequently, the thesis concludes that Humeanism and dispositionalism are on a par as regards the remaining charge of humility. Unorthodox Humeanism provides a competitive and adequate ontology in the light of contemporary science.