There are a few examples in the literature of metals that, in the T 0 K limit, show a resistivity that rises with decreasing temperature without any sign of either saturation or a gap. Well known cases include underdoped cuprates in high magnetic fields and some doped uranium heavy fermion compounds. I will review these and some less-well-known cases, before describing the behaviour of FeCrAs , in which we find a continuously rising resistivity from 900 K down to below 50 mK, with a brief interruption due to an antiferromagnetic transition at about 100 K. Down to at least 50 mK the resistivity is nearly linear in temperature, but with a negative coefficient. We speculate that this behaviour may be connected to fluctuations of frustrated iron “trimers” that do not order magnetically. 1. W. Wu, A. McCollam, P.M.C. Rourke, D. Rancourt, I. Swainson and S.R. Julian, in preparation.