Feedback plays a fundamental role in determining the properties of galaxies. In particular, dwarfs in the Local Group of galaxies are ideal places to test the physics of star formation and the role of stellar and supernova feedback. Recent advances in the modeling of dwarfs have allowed simulators to explain a number of long-standing puzzles related to dwarf galaxy observations (like the existence of bulgeless disks and dark matter cores). I will present results from high resolution, fully cosmological simulations of dwarf galaxies that successfully match observational trends, and use them to explain and explore a number of puzzles presented by dwarf galaxy observations. I will explain the role of feedback in the Stellar to Halo Mass (SMHM) relationship, how it contributes to scatter at the low mass end, and the ramifications of this scatter on the stellar mass function as well as the distribution of satellites around dwarf galaxies. I will also show that the same feedback processes that act to create dark matter cores also expand stellar orbits which allows the simulations to match observed dwarf galaxy gradients. In fact, I will show that dwarf galaxies form from the inside-out, despite appearing to form from the outside-in.