  We review the use of Cepheids as distance indicators with particular emphasis
on the methods which have been applied to HST observations of Cepheids. The
calibration of the period-luminosity relations is examined in detail and we
identify possible problems with the existing calibrations. New V- and I-band
period luminosity relations are presented based on a sample of 53 Cepheids in
the LMC with photometry drawn from the literature. These revised PL relations
result in a systematic decrease of approx 0.1 magnitudes in distance moduli
derived using the standard method of extinction correction. Hence estimates of
the Hubble constant based on such distances should be increased by $\sim5%$.
Other aspects of Cepheid distance determination, specifically incompleteness
bias, metallicity dependence, the effects of crowding and contamination of
samples by non-Cepheids are also discussed. We conclude that current HST
distance estimates to individual galaxies are probably good to about 10%, but
that much of this error is systematic. Efforts to reduce the systematics,
therefore, for example by improving the photometric calibration, refining the
distance to the LMC, and reobserving the Cepheid galaxies in the infrared with
NICMOS, will give large returns.
