  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
$0<z\lesssim6$, and it can be used to constrain the evolution of the luminosity
function (LF) for star forming (SF) galaxies. The LF evolution for SF galaxies
has been previously explored using optical source counts, as well as radio
source counts at 1.4 GHz, and a well-known degeneracy between luminosity
evolution ($L\propto(1+z)^Q$) and density evolution ($\phi\propto(1+z)^P$) is
found. Combining the constraints from the global SFR density evolution with
those from the 1.4 GHz radio source counts at sub-millijansky levels allows
this degeneracy to be broken, and a best fitting evolutionary form to be
established. The preferred evolution in a $H_0=70, \Omega_M=0.3,
\Omega_\Lambda=0.7$ cosmology from these combined constraints is
$Q=2.70\pm0.60$, $P=0.15\pm0.60$.
