Rigidity theory is an extraordinary tool to understand glasses. This article demonstrates how this model can help in understanding the link between structure, dynamics, and subtler properties such as drift and aging, in particular, in phase-change materials (PCMs). First, a map of flexible/rigid regions in the Ge-(Sb)-Te system is drawn on the basis of atomistic structures modeled either by ab initio or reverse Monte Carlo techniques. A clear link between the flexible/rigid nature of the glass and its aging behavior is shown through resistivity drift as a function of composition measurements in amorphous GexTe100–x. In the particular case of amorphous GeTe, application of rigidity theory indicates that the average number of mechanical constraints decreases during aging, making the glass less stressed-rigid. Finally, the stability of PCMs also depends on the topology of the materials. The increasing number of constraints in GeTe when doped with C or N results in increased stability of the PCM.