Amorphous solids manifest puzzling effects of mysterious degrees of freedom that give rise to a heat capacity and phonon scattering in great excess over what would be expected for a solid that has a unique vibrational ground state. Of particular conceptual importance is the apparent near universality of phonon scattering in amorphous solids made by quenching a liquid. To rationalise this universality, scale-free scenarios have been proposed that either hinge on there being long-range interactions between bare structural degrees of freedom or that invoke long-range criticality stemming from the emergence of marginally stable vibrational modes. In a contrasting, local scenario, the puzzling low-temperature degrees of freedom are, instead, weakly-interacting, strongly anharmonic degrees of freedom each of which involves the motion of a few hundred particles. In this scenario, the universality of phonon scattering comes about because the characteristic energy scale of the local anharmonic resonances and the strength of their interaction with phonons are both set by the glass transition temperature , while their concentration is set by the cooperativity size for dynamics at . The nanoscopic length is manifested in vibrational excitations of the spatial boundary of the resonances, which underlie the so-called Boson peak, and very deep, topological midgap electronic states in glassy semiconductors, which are implicated in a number of strange optoelectronic phenomena in amorphous chalcogenides. I discuss the merits of the above scenarios when confronted with experimental data.