  One of the most exciting and pressing issues in cosmology today is the
discrepancy between some measurements of the local Hubble constant and other
values of the expansion rate inferred from the cosmic microwave background
(CMB) radiation. Resolving these differences holds the potential for the
discovery of new physics beyond the standard model of cosmology: Lambda Cold
Dark Matter (LCDM), a successful model that has been in place for more than 20
years. Given both the fundamental significance of this outstanding discrepancy,
and the many-decades-long effort to increase the accuracy of the extragalactic
distance scale, it is critical to demonstrate that the local measurements are
convincingly free from residual systematic errors. We review the progress over
the past quarter century in measurements of the local value of the Hubble
constant, and discuss remaining challenges. Particularly exciting are new data
from the James Webb Space Telescope (JWST). JWST is delivering high-resolution
near-infrared imaging data to both test for and to address directly several of
the systematic uncertainties that have historically limited the accuracy of the
extragalactic distance scale. We present an overview of our new JWST program to
observe Cepheids, TRGB and JAGB stars. For the first galaxy in our program, NGC
7250, the high-resolution JWST images demonstrate that many of the Cepheids
observed with the Hubble Space Telescope (HST) are significantly crowded by
nearby neighbors. Avoiding the more significantly crowded variables, the
scatter in the JWST near-infrared (NIR) Cepheid period-luminosity relation is
decreased by a factor of two compared to those from HST, illustrating the power
of JWST for improvements to local measurements of Ho. Ultimately, these data
will either confirm the standard model, or provide robust evidence for the
inclusion of additional new physics.
