Several of the greatest mysteries in fundamental physics center on large hierarchies of scales.These include central problems in particle physics (like the electroweak hierarchy problem) and in cosmology (like the cosmological constant problem, and the puzzle of why the geometry of our universe is so homogeneous, isotropic, and flat). I describe some models in quantum field theory and string theory which may explain these puzzles, and which will be tested in the near future with the LHC and Planck satellite. These models are motivated by clashing notions of "naturalness" in theoretical physics, and near term experiments may confirm or overthrow some of these notions.