1.1. Peculiar Velocities versus H0
What it means to ``measure a galaxy's distance'' depends on whether one is interested in studying peculiar velocities or determining the value of the Hubble constant. A galaxy's peculiar velocity may be estimated given its ``distance'' in km s-1 - the part of its radial velocity due solely to the Hubble expansion. The same object provides an estimate of H0 only if one can measure its distance in metric units such as megaparsecs. What this means in practice is that accurate peculiar velocity studies may be carried out today, despite the fact that H0 remains undetermined at the ~ 20% level.
Another basic distinction between velocity analysis and
the search for H0 concerns the distance regimes in which they
are optimally conducted. Peculiar velocity surveys are best
carried out in the ``nearby'' universe, where peculiar velocity errors
are comparable to or less than the peculiar velocities themselves.
The characteristic amplitude of the
radial peculiar velocity, vp, is a few hundred km
s-1 at all distances, whereas the errors we make in estimating
vp
grow linearly with distance (Section 3).
It turns out that the ``break-even'' point occurs
at distances of ~ 5000 km s-1. Although we may hope to glean
some important information (such as bulk flow amplitudes) on
larger scales, our ability to construct an accurate picture
of the velocity field is restricted to the region within about
50h-1 Mpc.
In the Hubble constant problem, by contrast,
peculiar velocities are basically a nuisance. We would like them to
be a small fraction of the expansion velocity, so that
we incur as small as possible an error by neglecting them.
This is best achieved by using comparatively distant
objects, d 
7000
km s-1, as tracers of the expansion.
On the other hand, to obtain the absolute distances
needed to measure H0, we must first calibrate our distance
indicators locally (
2000 km s-1). This is because
the distance indicators capable of reaching the ``far field'' (
7000 km s-1) of the Hubble flow generally have no a priori
absolute calibration (cf. Section 1.2).
The only reliable distance indicator that
can bridge the gap between the Milky Way and the handful of
Local Group galaxies whose absolute distances are well-known,
and galaxies beyond a few Mpc,
is the Cepheid variable method (Section 2), which
is limited to distances
2000 km s-1. As a result, Hubble
constant measurement is inherently a two-step process: local
calibration in galaxies with Cepheid distances,
followed by distance measurements in the far field where
the effect of peculiar velocities is small.
The local calibration
step is unnecessary in peculiar velocity studies.
Although peculiar velocity surveys and H0 measurement differ in the ways just discussed, the two problems are, ultimately, closely related. Many distance indicator methods have been and are being used for both purposes. Indeed, a distance indicator calibrated in km s-1 may be turned into a tool for measuring H0 simply by knowing the distances in Mpc to a few well-studied objects to which it has been applied. This Chapter will thus be organized not around the peculiar velocity-H0 distinction, but rather around methods of distance estimation.