Extragalactic variables and their application to cosmology

I will present results from two ongoing projects: a search for Miras in M33 using a novel periodogram technique, and a determination of the Hubble constant with a total uncertainty of ~2.5% based on Cepheid distances to 18 hosts of type Ia supernovae. I will discuss the implications of the former for LSST, and future steps for the latter in the era of Gaia and JWST.