Observations show that the Universe is fully ionized by z~6. The LyC photons from dwarf galaxies have been suggested as the most promising source of reionization, but little is yet known about how they escape from their host dark matter halos. In this talk, I will discuss two mechanisms (supernova feedback and runaway stars) that regulate the escape fraction at the epoch of reionization (z>7) by using high-resolution, cosmological radiation hydrodynamics simulations with adaptive mesh refinement. We find that a rapid build-up and subsequent destruction of star-forming clouds by SNe allows for the LyC photons to escape efficiently (~10%) through low-density channels. Inclusion of runaway OB stars further enhances the fraction (~14%), but the total number of escaping photons is found to be similar due to more effective suppression of star formation in this case. Both models (SN or SN+runaways) predict that a sufficient number of photons escapes from the halo at z~7 to keep the universe ionized, as observed. However, a still larger amount of ionizing photons appears necessary at z>9 to accommodate the electron optical depth inferred from the CMB measurements. I will finish the talk by discussing two possible solutions to this problem.