The theory of how turbulent energy decays via a Richardson cascade is well-established for classical fluids, and it also seems to apply to the case of so-called co-flowing He II turbulence in the range from the superfluid transition temperature T_lambda down to ~1 K, where its behaviour is similar to that of a classical fluid. For pure superfluids, e.g. He II in the mK range or 3He-B in the microK range, where the normal fluid density rho_n is near zero, the mode(s) through which quantum turbulence (QT) might decay have been much less clear because of the absence of viscosity to dissipate the turbulent energy on small length scales. Recent advances made in the theory of QT in this T-tends-tozero limit are consistent with such experimental evidence as is available, but new experiments supported by new techniques for the production and detection of QT are urgently required. The experimental situation is reviewed and prospects for further advances are considered.