A buyer's guide to the Hubble Constant

Since the expansion of the universe was first established by Edwin Hubble and Georges Lemaitre about a century ago, the Hubble constant H0 which measures its rate has been of great interest to astronomers. Besides being interesting in its own right, few properties of the universe can be deduced without it. In the last decade a significant gap has emerged between different methods of measuring it, some anchored in the nearby universe, others at cosmological distances. The SH0ES team has found $H_0 = 73.2 \pm 1.3$ km sec$^{-1}$ Mpc$^{-1}$ locally, whereas the value found for the early universe by the Planck Collaboration is $H_0 = 67.4 \pm 0.5$ km sec$^{-1}$ Mpc$^{-1}$ from measurements of the cosmic microwave background. Is this gap a sign that the well-established $Λ$CDM cosmological model is somehow incomplete? Or are there unknown systematics? And more practically, how should humble astronomers pick between competing claims if they need to assume a value for a certain purpose? In this article, we review results and what changes to the cosmological model could be needed to accommodate them all. For astronomers in a hurry, we provide a buyer's guide to the results, and make recommendations.