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 (EoR): 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 observations of the redshifted 21-cm line: providing a 3D map of the first billion years of our Universe. The patterns in these maps are driven by UV and X-ray radiation from the first galaxies, as well as physical cosmology. I will showcase a Bayesian, data-driven, forward-modeling framework to understanding astrophysics and cosmology from the Cosmic Dawn. I will demonstrate how preliminary 21-cm data from the Hydrogen Epoch of Reionization Array (HERA), when combined with other EoR and galaxy observations, already constrain the heating and ionization history of the Universe. High mass X-ray binaries (HMXBs) are mostly likely responsible for heating the intergalactic medium before the EoR, and current HERA limits imply that the first HMXBs were more luminous than local ones, consistent with theoretical arguments based on binary evolution in low metallicity environments.