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 observed temperature and polarization fluctuations in 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 (ΛCDM), 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), for which we present an overview of our program and first results. We focus in particular on Cepheids and the Tip of the Red Giant Branch (TRGB) stars, as well as a relatively new method, the JAGB (J-Region Asymptotic Giant Branch) method, all methods that currently exhibit the demonstrably smallest statistical and systematic uncertainties. 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 extragalactic distance scale measurements (e.g., the dimming effects of interstellar dust, chemical composition differences in the atmospheres of stars, and the crowding and blending of Cepheids contaminated by nearby previously unresolved 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 PL relation is decreased by a factor of two compared to those from HST, illustrating the power of JWST for improvements to local measurements of H 0. Ultimately, these data will either confirm the standard model, or provide robust evidence for the inclusion of additional new physics.