Within just the last few years, we have advanced from knowing only a few galaxies at z>2 to having redshifts for nearly 1000 z~2-5 objects. The majority of this sample has been detected through the photometric ``drop-out'' technique used so successfully by Steidel and his collaborators. In addition, a handful of objects have already been detected at z>5, and we may already have a few objects at z>6! These data, plus that at z<2 have resulted in a characterization of the star formation history of the universe, commonly known as the ``Madau plot'', which gives SFR per comoving volume vs redshift from the present day at z=0 to z~5. Recently, we have realized that dust has significantly affected our SFR estimates for the objects that have been detected in the optical, and have developed approaches to correct for that extinction. We now also have increasingly good evidence that a substantial fraction (>50%?) of the high redshift star formation occurs in dust-enshrouded starbursts that were detected at 850 micron with a submm bolometer SCUBA on the JCMT telescope. These objects will typically be too faint to detect and measure redshifts in the optical, though those that can have already provided valuable constraints. The highest redshift objects at z~5 and beyond are intriguing sources, but test even the limits of Keck and of HST. The detailed study of such sources may well only be practical for gravitationally-lensed objects, where the high magnification allows for a much more detailed study of the proto-galaxy's structure, until even larger space-based (NGST) and ground-based (30-m plus) telescopes are developed.

20 pages(latex), 5 figures(eps), 2 color images(jpg) Conference: "Toward a New Millennium in Galaxy Morphology"