The melting of stable glasses is governed by nucleation-and-growth dynamics.

We discuss the microscopic mechanisms by which low-temperature amorphous states, such as ultrastable glasses, transform into equilibrium fluids, after a sudden temperature increase. Experiments suggest that this process is similar to the melting of crystals, thus differing from the behaviour found in ordinary glasses. We rationalize these observations using the physical idea that the transformation process takes place close to a "hidden" equilibrium first-order phase transition, which is observed in systems of coupled replicas. We illustrate our views using simulation results for a simple two-dimensional plaquette spin model, which is known to exhibit a range of glassy behaviour. Our results suggest that nucleation-and-growth dynamics, as found near ordinary first-order transitions, is also the correct theoretical framework to analyse the melting of ultrastable glasses. Our approach provides a unified understanding of multiple experimental observations, such as propagating melting fronts, large kinetic stability ratios, and "giant" dynamic length scales. We also provide a comprehensive discussion of available theoretical pictures proposed in the context of ultrastable glass melting.