Efforts to make existing separation methods more efficient and eco-friendly may get a boost from the use of a relatively new class of compounds known as ionic liquids (ILs). The separation of azeotropic mixtures has conventionally been one of the most challenging tasks in industrial processes due to the fact that their separation by simple distillation is basically impossible. This paper provides a critical review of methods using ILs as azeotrope breakers. Three separation processes were addressed: liquid-liquid extraction, extractive distillation, and supported liquid membranes. We examine the azeotrope breaking potential of ILs and compare their performance to that of conventional solvents. A systematic analysis of the influence of the structure of ILs on their azeotrope breaking capacity contributes to the establishment of guidelines for selecting the most suitable ILs for the separation of specific azeotropic mixtures.