Seven zoonoses — human infections of animal origin — have emerged from the Coronaviridae family in the past century, including three viruses responsible for significant human mortality (SARS-CoV, MERS-CoV, and SARS-CoV-2) in the past twenty years alone. These three viruses, in addition to two older CoV zoonoses (HCoV-229E and HCoV-NL63) are believed to be originally derived from wild bat reservoir species. We review the molecular biology of the bat-derived Alpha- and Betacoronavirus genera, highlighting features that contribute to their potential for cross-species emergence, including the use of well-conserved mammalian host cell machinery for cell entry and a unique capacity for adaptation to novel host environments after host switching. The adaptive capacity of coronaviruses largely results from their large genomes, which reduce the risk of deleterious mutational errors and facilitate range-expanding recombination events by offering heightened redundancy in essential genetic material. Large CoV genomes are made possible by the unique proofreading capacity encoded for their RNA-dependent polymerase. We find that bat-borne SARS-related coronaviruses in the subgenus Sarbecovirus, the source clade for SARS-CoV and SARS-CoV-2, present a particularly poignant pandemic threat, due to the extraordinary viral genetic diversity represented among several sympatric species of their horseshoe bat hosts. To date, Sarbecovirus surveillance has been almost entirely restricted to China. More vigorous field research efforts tracking the circulation of Sarbecoviruses specifically and Betacoronaviruses more generally is needed across a broader global range if we are to avoid future repeats of the COVID-19 pandemic.