  The star formation history derived from ultraviolet and H$\alpha$ data,
without correction for dust extinction, on the one hand, and from far infrared
and submillimetre data, on the other, is investigated. The latter estimates are
found to be a factor 2-3 higher than the former, consistent with 2/3-3/4 of the
uv light in star forming regions being absorbed by dust and reemitted in the
far infrared. A reanalysis of the Hubble Deep Field galaxies using photometric
reshifts shows no evidence for a decline in star formation rate at z = 2-4.
  A simple and versatile parameterized approach to the star formation history
allows a quantitative investigation of the constraints from far infrared and
submillimetre counts and background intensity measurements. A good fit to the
counts, the 850 $\mu$m background and the star formation history can be found
in an $\Omega_o$ = 1 universe, but this model fails to account for even the
lowest estimates of the 140-350 $\mu$m background by a factor of 2. Either the
observed values are overestimated or we need a new population of found in a
$\Lambda$ = 0, $\Omega_o$ = 0.3 universe.
