  Radiative transfer simulations are now at the forefront of numerical
astrophysics. They are becoming crucial for an increasing number of
astrophysical and cosmological problems; at the same time their computational
cost has come to the reach of currently available computational power. Further
progress is retarded by the considerable number of different algorithms
(including various flavours of ray-tracing and moment schemes) developed, which
makes the selection of the most suitable technique for a given problem a
non-trivial task. Assessing the validity ranges, accuracy and performances of
these schemes is the main aim of this paper, for which we have compared 11
independent RT codes on 5 test problems: (0) basic physics, (1) isothermal H II
region expansion and (2) H II region expansion with evolving temperature, (3)
I-front trapping and shadowing by a dense clump, (4) multiple sources in a
cosmological density field. The outputs of these tests have been compared and
differences analyzed. The agreement between the various codes is satisfactory
although not perfect. The main source of discrepancy appears to reside in the
multi-frequency treatment approach, resulting in different thicknesses of the
ionized-neutral transition regions and different temperature structure. The
present results and tests represent the most complete benchmark available for
the development of new codes and improvement of existing ones. To this aim all
test inputs and outputs are made publicly available in digital form.
