The spectral energy distributions (SEDs) of dusty high-redshift galaxies are poorly sampled in frequency and spatially unresolved. Their form is crucially important for estimating the large luminosities of these galaxies accurately, for providing circumstantial evidence concerning their power sources, and for estimating their redshifts in the absence of spectroscopic information. We discuss the suite of parameters necessary to describe their SEDs adequately without introducing unnecessary complexity. We compare directly four popular descriptions, explain the key degeneracies between the parameters in each when confronted with data, and highlight the differences in their best-fitting values. Using one representative SED model, we show that fitting to even a large number of radio, submillimetre and far-infrared (far-IR) continuum colours provides almost no power to discriminate between the redshift and dust temperature of an observed galaxy, unless an accurate relationship with a tight scatter exists between luminosity and temperature for the whole galaxy population. We review our knowledge of this luminosity-dust temperature relation derived from three galaxy samples, to better understand the size of these uncertainties. Contrary to recent claims, we stress that far-IR-based photometric redshifts are unlikely to be sufficiently accurate to impose useful constraints on models of galaxy evolution: finding spectroscopic redshifts for distant dusty galaxies will remain essential.
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