  We constrain the isotropic luminosity function (LF) and formation rate of
long gamma-ray bursts (GRBs) by fitting models 'jointly' to both the observed
differential peak flux and redshift distributions. We find evidence supporting
an evolving LF, where the luminosity scales as (1+z)^delta with an optimal
delta of 1.0\pm 0.2. For a single power-law LF, the best slope is ~ -1.57 with
an upper luminosity of 10^53.3 erg/s, while the best slopes for a double
power-law LF are approximately -1.6 and -2.6 with a break luminosity of 10^52.7
erg/s. Our finding implies a jet model intermediate between the universal
structured epsilon(theta) proportional to theta^-2 model and the
quasi-universal Gaussian structured model. For the uniform jet model our result
is compatible with an angle distribution between 2 and 15 grades. Our best
constrained GRB formation rate histories increase from z=0 to z=2 by a factor
of ~30 and then continue increasing slightly. We connect these histories to
that of the cosmic star formation history, and compare with observational
inferences up to z~6. GRBs could be tracing the cosmic rates of both the normal
and obscured star formation regimes. We estimate a current GRB event rate in
the Milky Way of ~5 10^-5 yr^-1, and compare it with the birthrate of massive
close WR+BH binaries with orbital periods of hours. The agreement is rather
good suggesting that these systems could be the progenitors of the long GRBs.
