  New bolometer arrays operating on the world's largest sub-mm and mm
telescopes offer a unique view of the high-redshift universe with unprecedented
sensitivity. Recent sub-millimetre continuum studies show that the host
galaxies of many luminous high-redshift AGN (radio galaxies and radio-quiet
quasars) radiate strongly at rest-frame far-infrared wavelengths and thus
contain substantial quantities of dust. In the majority of these high-redshift
AGN-hosts, the inferred star formation is proceeding at a rate comparable to
that found in local, interacting ultra-luminous FIR galaxies. This level of
activity is an order of magnitude greater than the more modest star-formation
rates apparently displayed by the recently-discovered Lyman-limit galaxies at z
~ 3, which have been argued to represent the era of spheroid formation
(although the degree to which the effects of reddening by dust grains may have
biased the interpretation of these optical/UV studies of high-z galaxies has
yet to be properly determined). However, it is too early to say whether such
bright FIR emission is a feature of all massive galaxies at z > 3, or whether
it is in fact confined to the hosts of the most luminous AGN.
  In this paper we review the current status of cosmological observations at
sub-mm and mm wavelengths, highlighting our own recent SCUBA observations of
high-redshift radio galaxies. We also explain how observations over the next
few years should allow the true level of star-formation activity in the high-z
universe to be properly quantified, and we provide example predictions for the
first deep sub-millimetre survey (of the Hubble Deep Field), which we and our
colleagues are currently undertaking with SCUBA at the JCMT.
