  The invariant cross sections for direct photon production in hadron-hadron
collisions are calculated for several initial energies (SPS, ISR, S$p \bar p$S,
RHIC, Tevatron, LHC) including initial parton transverse momenta within the
formalism of unintegrated parton distributions (UPDF). Different approaches
from the literature are compared and discussed. A special emphasis is put on
the Kimber-Martin-Ryskin (KMR) distributions and their extension into the soft
region. Sum rules for UPDFs are formulated and discussed in detail. We find a
violation of naive number sum rules for the KMR UPDFs. An interesting interplay
of perturbative (large $k_t^2$) and nonperturbative (small $k_t^2$) regions of
UPDFs in the production of both soft and hard photons is identified. The
$k_t$-factorization approach with the KMR UPDFs is inconsistent with the
collinear approach at large transverse momenta of photons. Kwieci\'nski UPDFs
provide very good description of all world data, especially at SPS and ISR
energies. Off-shell effects are discussed and quantified. Predictions for the
CERN LHC are given. Very forward/backward regions in rapidity at LHC energy are
discussed and a possibility to test unintegrated gluon distributions (UGDF) is
presented.
