The origin of the late-time cosmic acceleration is one of the most intriguing problems of modern physics; the standard theoretical explanation requires extreme fine-tuning to match observations. Resolution of this puzzle may require modifications to either the assumption that all matter has positive pressure or to the theory of gravity itself on cosmological distance scales. In this dissertation we explore the viability of several promising modifications to gravity unified by the presence of a Vainshtein-type screening mechanism suppressing the modifications within the solar system. In order to remain theoretically and observationally viable, a theory of modified gravity must: 1. be free of unphysical degrees of freedom that lead to instabilities, 2. produce a stable phase of cosmic acceleration, 3. allow stable field configurations around astrophysical objects, and 4. be consistent with measured limits on the strength of fifth forces in various environments. We study three models: that of a scalar called the galileon that mediates a gravitational-strength fifth force, a braneworld-inspired theory of multiple galileons, and the theory of a massive graviton coupled to a galileon. We show that the massive graviton -- galileon theory satisfies the first condition for viability but fails the second and that the multi-galileon theory fails the third condition. The theory of a single galileon satisfies the first three conditions; the last is known to be satisfied in the case of an isolated object. We develop a formalism to make more precise predictions regarding the galileon forces in multi-body systems. Finally, we consider the topological defect solutions of more general scalar theories with noncanonical kinetic terms and show that domain walls can mimic the field profile and energy density of a canonical domain wall, though the two are distinguishable by their fluctuation spectra.