From powering the supermassive black holes in the centers of galaxies to forming the building blocks of planets and planetary systems, accretion disks are ubiquitous throughout the universe. Given this prevalence and parallel advances in computational astrophysics and observational capabilities, now is the quintessential time to understand how these complex systems work in their various guises. In this talk, I will present my vision for combining observational and theoretical tools to answer key questions related to both protoplanetary disks and high-energy disks around black holes. I will begin with an overview of accretion theory, describing the angular momentum transport problem in astrophysical disks, and how I am using sophisticated numerical simulations to solve this issue. I will then put this problem within the context of planet formation by describing how I am using numerical simulations as well as observations with the Atacama Large Millimeter/submillimeter Array (ALMA) to test current models and build a new paradigm for protoplanetary disk evolution. Finally, I will discuss theoretical work on the formation of planetary building blocks, called planetesimals, within the gas disk environment implied by observations and how the predicted properties of these planetesimals compare with those observed in the asteroid and Kuiper Belt planetesimal populations.