The principle cause of frost heave is the formation of segregated ice—ice lenses—in freezing soil columns. Despite much experimental and theoretical work, there remain many questions about the fundamental process by which this occurs. Frost-heave models fall into two main classes: capillary and frozen-fringe models. Which model is appropriate depends on whether there is a frozen fringe; these are difficult to observe but some experimental evidence does exist. Recent advances have revitalized the capillary model, such as the engulfment model and the concept of geometrical supercooling. Key experimental and theoretical challenges remain to be resolved.