For all the successes of the two edifices of modern physics, quantum theory and Einstein's relativity, a fundamental description of the Universe as a whole -- a theory that informs as to the true nature of reality -- has continued to elude science. This thesis describes the development and evolution of a new paradigm called Process Physics, a radical information-theoretic modelling of reality. It is argued that the failure of the extant approaches in physics is the direct consequence of limitations stemming from the mathematization, language and methodology of theoretical physics: the limitations of the postulated background spatial concepts and geometric modelling of time, the limitations of quantum theory in its failure to account for the measurement process and classicality; and the limitations of formal systems. In contrast, Process Physics utilizes the limitations of logic first identified by Godel and asserts the priority of process and relational endophysics, realized via a stochastic, autopoietic bootstrap system whose properties emerge a posteriori rather than being assumed a priori. The work is arranged in two parts. Part I discusses the historical, philosophical, and metaphysical foundations of physics to consider how the prevailing views in modern physics arose and what this revealed and contributed to the development of Process Physics. Part II describes the fundamentals of the new theory and its implementation, and demonstrates the viability of looking outside the current paradigms by showing that Process Physics yields unified emergent phenomena that permit an understanding of fundamental processes and penultimately motivate both quantum theory and relativity as relevant higher-level descriptors within their respective domains.