Exercising control over the formation of ice and similar crystalline structures is important in avariety of contexts, from preserving organs for transplant to preventing clathrate hydrate plugs in natural gas pipelines. To achieve this control, it is crucial to understand nucleation phenomena at the molecular level. Studies have shown that heterogeneous nucleation proceeds orders of magnitude faster than homogeneous nucleation. Hence an understanding of ice nucleation phenomena in most real-world contexts hinges upon identifying the molecular-scale features of surfaces that inhibit (or even promote) heterogeneous ice nucleation. Yet the combination of molecular-scale characteristics that determines the ice nucleation propensity of a given material remain poorly understood. We approach this challenge from a thermodynamic perspective, with the goal of understandingicephilicity : the preference of a heterogeneous solid surface (or macromolecule) for ice over liquid water. Recent work has shown that there is a complex interplay between a surface's morphology and its icephilicity: small variations in properties (such as surface exibility and lattice mismatch) can signicantly impact a material's ability to interact favorably with ice. We have developed novel approaches for characterizing surface icephilicity, and applied them to study a wide range of materials using molecular simulations and enhanced sampling techniques. Our results shed new light on the molecular-scale features that govern a material's propensity to nucleate (or inhibit) ice and related crystalline structures.