The Universe changed drastically during its first billion years as neutral hydrogen gas, which filled the intergalactic space, became ionized. This last major phase transition of the Universe is an important cosmological period known as the Epoch of Reionization. Simulations and observations seem to indicate that primordial galaxies were the main sources of the ionizing UV photons responsible for Reionization. However, many unknowns remain on the mechanisms that enabled these photons to escape the neutral interstellar medium of galaxies and ionize the space around them on much larger scales. Here, I will show how observations of nearby Lyman-Continuum emitting galaxies can be used to gain insights on the physical processes that caused cosmological reionization. In particular, I will describe results from the LzLCS and LaCOS programs, that are investigating the global and resolved galaxy properties connected with Lyman Continuum emission in the low-redshift Universe. I will also discuss what observations of the neutral gas reservoirs of Lyman Continuum emitters teach us about the potential role of galaxy interactions during the Epoch of Reionization.