Traditional physics suggests that history is merely the uncoiling of the Big Bang, but is this reductionism sufficient to explain our experience of the real world? The concept of emergent phenomena is a fresh response to the development of complexity in the universe. This thesis reviews the complexity that has emerged in the universe, which many have found so surprising and unexpected. It introduces the idea of top-down causation to supplement lower-level laws of physics and generate the emergence of complexity. It reviews the foundations of quantum mechanics, focusing on how quantum randomness may provide the freedom that enables such higher-level laws to imbue the universe with creativity. It then critically analyzes the uniqueness theorems that underlie the initial value problems of traditional physics and demonstrate exceptions to them. Finally, it demonstrates the coherence of higher-level laws by explicitly creating models of emergent phenomena and top-down causation, in simple example universes. In the models, a new higher-level law must immediately accompany the emergence of each new phenomenon. Future work would involve constructing models testable in the real world.