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Population genomics is a dramatically expanding field fueled by the dramatic reduction in cost of DNA sequencing. Using increasingly sophisticated inference methods it is now possible to use such data to uncover new insights about human history and evolution. One of the most promising developments in this field in recent years has been the emergence of methods for inferring genetic genealogies from large sets of individual genomes. These genetic genealogies are represented by ancestral recombination graphs (ARGs). For decades the ARG has served as a fundamental modeling tool in population genetics, but its complex correlation structure and high level of uncertainty make ARG inference notoriously difficult. This is now changing, with several methods developed to tackle this challenging task. In my talk I will introduce the problem of ARG inference and present a study conducted by my research group a few years ago that used inferred ARGs to uncover hidden genetic interactions between our ancestors and Neanderthals more than 100,000 years ago.