A discussion is given of ferroelectrics (FEs) that have their Curie temperatures Tc very near absolute zero. These have differences in their dynamics in comparison with higher-temperature systems, since domain wall motion occurs via quantum mechanical tunneling and not by thermally activated diffusion. Emphasis in the present paper is on FEs that have relaxor characteristics. In such systems, the temperature at which the isothermal electric susceptibility ε(T,f) peaks is a strong function of frequency, and it decreases with decreasing frequency. This is due to glassy viscosity and is symbolic of non-equilibrium dynamics, usually described by a Vogel-Fulcher equation. It permits an extra dimension with which to examine the transitions. The second half of this paper reviews domain wall instabilities and asks about their presence in QCP ferroelectrics, which has not yet been reported and may be unobservable due to the absence of thermal diffusion of walls near T = 0; in this respect, we note that diffusion does exist in ferroelectric relaxors, even at T = 0, by virtue of their glassy, viscous dynamics.