  In this presentation I summarize recent work on Cepheid research carried out
at the National Central University. The mid-infrared period-luminosity (P-L)
relations for Cepheids are important in the James Webb Space Telescope era for
distance scale work, as the relations have potential to derive the Hubble
constant within ~2% accuracy - a critical constraint in the precision
cosmology. Consequently, we have derived the mid-infrared P-L relations for
Cepheids in the Large and Small Magellanic Clouds, using archival data from the
Spitzer Space Telescope. Kepler Space Telescope is a NASA mission to search for
Earth-size and larger planets around Sun-like stars, by observing continuously
the stars in a dedicated patch of the sky. As a result, the almost
un-interrupted observation is also used for stellar variability and
asteroseismological study. However, Kepler observations are carried out with a
single broad-band filter, hence ground-based follow-up observation needed to
complement Kepler light curves to fully characterize the properties of the
target stars. Here I present the ground-based optical follow-up observations
for two Cepheid candidates located within the Kepler's field-of-view. Together
with Kepler light curves, our ground-based data rule out V2279 Cyg being a
Cepheid. Hence V1154 Cyg is the only Cepheid in the Kepler's field.
