Superionic conductors are sparking tremendous interest in multiple fields. While fast ionic conductors are searched for solid state batteries, they also often possess low lattice thermal conductivities essential for high thermoelectric efficiencies. In fact, many Ag + and Cu + superionic thermoelectric materials have thermal conductivities below the theoretical "minimum" thermal conductivity for solids, leading some to the suggestion that ion mobility makes these materials more liquid-like. However, no physical connections between thermal and ionic transport have thus far been shown. Recently, a foundational misconception within the concept of "phonon liquid electron crystal" 2 was proven by showing that transverse phonon modes, which should not exist in a liquid, do persist above superionic phase transitions in solids. Concurrently, a universal theory for heat conduction in solids has been developed that suggests low thermal conductivities can arise solely from (static) atomic disorder, strong anharmonicity and/or complex unit cells, all of which are inherent to fast ion conducting materials. Lacking a direct comparison between ionic transport data and the thermal and vibrational properties in these systems, the interdependence of both transport processes remains elusive.