Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters.Recent advances relating to ion conduction in glasses and other disordered solids include the application of multidimensional NMR techniques [1], the introduction of ac nonlinear spectroscopy [2], and elucidations of the high-frequency nearly constant loss [3]. Moreover, it was found that the old idea of ions moving by the vacancy mechanism may well be correct [4], and simulations gave new insight into the mixed-alkali effect [5]. Despite these and other significant advances, important questions remain unanswered. For instance, it is still not understood what role is played by ion interactions for the conductivity [6], or why the random barrier model (RBM) [7,8] represents ac conductivity data so well. The latter question is not answered below, but new simulations and arguments are presented that we believe lead to a full understanding of the physics of the RBM in the extreme disorder limit (low temperature limit).Ac conductivity is often studied also for amorphous semiconductors, electronically or ionically conducting polymers, defective crystals of various kinds, polaronic conductors, etc [7,8]. It is a longstanding observation that all disordered solids have remarkably similar ac conductivities [9]. Universal features include [8]: At low frequencies the conductivity is constant. At higher frequencies it follows an approximate power law with an exponent less than one that increases slightly with increasing frequency. When measured in a fixed frequency range, the exponent converges to one as temperature goes to zero. The ac conductivity is less temperature dependent than the dc conductivity and obeys time-temperature superposition (sometimes referred to as "scaling"). The frequency marking onset of ac conduction, ω m , has the same activation energy as the dc conductivity.These and other observed features are reproduced by the RBM characterized [8,10] by five assumptions: 1) All charge carrier interactions including self-exclusion are ignored; 2) Charge carrier motion takes place on a cubic lattice; 3) All lattice sites have same energy; 4) Only nearest-neighbor jumps are allowed; 5) Jump rates ∝ exp(−E/k B T ) have random activation energies with distribution p(E). In the RBM the ac conductivity σ(ω) relative to σ(0) as a function of a suitably scaled frequency becomes independent of p(E) in the extreme disorder limit, i.e., when the width of p(E) is much larger than k B T [8]. Despite lack of non-trivial free parameters the RBM universal ac conductivity gives a good fit to experiment [8]; more refined models yield results that are close to those of the RBM [11].It is well-known t...