If high-redshift galaxies resemble rapidly star-forming galaxies in the loc
al universe, most of the luminosity produced by their massive stars will ha
ve been absorbed by dust and reradiated as far-infrared photons that cannot
be detected with existing facilities. This paper examines what can be lear
ned about high-redshift star formation from the small fraction of high-reds
hift galaxies' luminosities that is emitted at accessible wavelengths. We f
irst consider the most basic ingredient in the analysis of high-redshift su
rveys: the estimation of star formation rates for detected galaxies. Standa
rd techniques require an estimate of the bolometric luminosity produced by
their massive stars. We review and quantify empirical correlations between
bolometric luminosities produced by star formation and the UV, mid-IR, sub-
mm, and radio luminosities of galaxies in the local universe. These correla
tions suggest that observations of high-redshift galaxies at any of these w
avelengths should constrain their star formation rates to within similar to
0.2-0.3 dex. We assemble the limited evidence that high-redshift galaxies o
bey these locally calibrated correlations. The second part of the paper ass
esses whether existing surveys have found the galaxies that host the majori
ty of star formation at high redshift even though they directly detect only
a small fraction of the luminosities of individual galaxies. We describe t
he characteristic luminosities and dust obscurations of galaxies at z simil
ar to 0, z similar to 1, and z similar to 3. After discussing the relations
hip between the high-redshift populations selected in surveys at different
wavelengths, we calculate the contribution to the 850 mum background from e
ach and argue that these known galaxy populations can together have produce
d the entire observed background. The available data show that a correlatio
n between star formation rate and dust obscuration L-bol,(dust)/L-UV exists
at low and high redshift alike. The existence of this correlation plays a
central role in the major conclusion of this paper: most star formation at
high redshift occurred in galaxies with moderate dust obscurations 1 less t
han or similar to L-bol,(dust)/L-UV, less than or similar to 100 similar to
those that host the majority of star formation in the local universe and t
o those that are detected in UV-selected surveys.