  We show that the use of red colour as the basis for selecting candidate high
redshift dusty galaxies from surveys made with Herschel has proved highly
successful. The highest redshift such object, HFLS3, lies at z=6.34 and
numerous other sources have been found. Spectroscopic followup confirms that
most of these lie at z>4. These sources are found in such numbers that they
represent a challenge to current models of galaxy evolution. We also examine
the prospects for finding dusty galaxies at still higher redshifts. These would
not appear in the SPIRE surveys from Herschel but would be detected in longer
wavelength, submm, surveys. Several such `SPIRE-dropouts' have been found and
are now subject to followup observations.
