Several experimental and theoretical studies conclude that the unconventional properties of bent-core nematics derive from cybotactic clusters, that is, very short-range correlation fluctuations of positional and orientational order. We show how X-ray diffraction from oxadiazole-based compounds strongly supports this model. Moreover, we recently reported an extraordinary magnetic-field-induced shift of both nematic-isotropic and smectic-C-nematic phase transition temperatures (T = 4K for B = 1 T). We review this effect, which is orders of magnitude larger than previously reported data, in the framework of the cybotactic model of bent-core nematics.