The birth of the first stars, black holes and galaxies heralded the end of the cosmic Dark Ages and the beginning of the Cosmic Dawn. The light from these objects heated and ionized almost every atom in existence, culminating in the Epoch of Reionization: the final major phase change of the Universe. This final frontier of astrophysical cosmology is undergoing a transition from an observationally-starved epoch to a "Big Data" field. This process is set to culminate with upcoming Square Kilometre Array observations of the redshifted 21-cm line: providing a 3D map of the first billion years of our Universe. Currently, we are starting to get a handle on the timing of reionization. However with the SKA, we will be able to actually study the UV and X-ray properties of the first galaxies, which are encoded in the large-scale structure of the H I signal. I will summarize the current state of knowledge about the epoch of reionization, and then introduce a Bayesian forward-modeling framework which will allow us to infer the properties of the unseen first galaxies from the 21-cm signal.