The evolution in the comoving space density of the global average galaxy star formation rate (SFR) out to a redshift around unity is well established. Beyond z~1 there is growing evidence that this evolution is flat or even increasing, contrary to early indications of a turnover. Some recent analyses of z~6 photometric dropouts are suggestive of a decline from z=3 to z~6, but there is still very little constraint on the extent of dust obscuration at such high redshifts. In less than a decade, numerous measurements of galaxy SFR density spanning z=0 to as high as z~6 have rapidly broadened our understanding of galaxy evolution, and a summary of existing SFR density measurements is presented here. This global star formation history compilation is found to be consistent to within factors of about three over essentially the entire range $0

15 pages, 5 figures, 4 tables, accepted for publication in ApJ