  Measurements of the Hubble constant, and more generally measurements of the
expansion rate and distances over the interval $0 < z < 1$, appear to be
inconsistent with the predictions of the standard cosmological model
($\Lambda$CDM) given observations of cosmic microwave background temperature
and polarization anisotropies. Here we consider a variety of types of
departures from $\Lambda$CDM that could, in principle, restore concordance
among these datasets, and we explain why we find almost all of them unlikely to
be successful. We single out the set of solutions that increase the expansion
rate in the decade of scale factor expansion just prior to recombination as the
least unlikely. These solutions are themselves tightly constrained by their
impact on photon diffusion and on the gravitational driving of acoustic
oscillations of the modes that begin oscillating during this epoch -- modes
that project on to angular scales that are very well measured. We point out
that a general feature of such solutions is a residual to fits to $\Lambda$CDM,
like the one observed in Planck power spectra. This residual drives the
modestly significant inferences of angular-scale dependence to the matter
density and anomalously high lensing power, puzzling aspects of a data set that
is otherwise extremely well fit by $\Lambda$CDM.
