  This paper examines what can be learned about high-redshift star formation
from the small fraction of high-redshift galaxies' luminosities that is emitted
at accessible wavelengths. 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
correlations suggest that observations of high-redshift galaxies at any of
these wavelengths should constrain their star-formation rates to within
0.2--0.3 dex. We assemble the limited evidence that high-redshift galaxies obey
these locally calibrated correlations. The characteristic luminosities and dust
obscurations of galaxies at z ~ 0, z ~ 1, and z ~ 3 are reviewed. After
discussing the relationship between the high-redshift populations selected in
surveys at different wavelengths, we calculate the contribution to the 850um
background from each. The available data show that a correlation between
star-formation rate and dust obscuration L_dust/L_UV exists at low and high
redshift. This correlation plays a central role in the major conclusion of this
paper: most star formation at high redshift occurred in galaxies with 1 <
L_dust/L_UV < 100 similar to those that host the majority of star formation in
the local universe and to those that are detected in UV-selected surveys.
(abridged)
