What is the likelihood that a hypothetical material -the combination of a composition and crystal structure -can be formed? Underpinning the reliability of predictions for local or global crystal stability is the choice of thermodynamic potential. Here, we discuss recent advances in free energy descriptions for crystals including both harmonic and anharmonic phonon contributions to the vibrational entropy. We critically discuss some of the techniques and descriptors, including data-driven machine learning approaches, being developed to assess the stability and synthesisability of solids. Avenues are highlighted that deserve further attention including thermodynamic and kinetic factors that govern the accessibility of metastable structures away from equilibrium.