Many industrial processes depend on efficient methods for separating azeotropic, close-boiling, or other low relative volatility mixtures. Ordinary distillation is typically either uneconomical or impossible in these cases. However, by adding specially chosen separating agents, the separation can generally be accomplished. The principal distillation-based techniques employed for separating such mixtures are discussed: extractive or homogeneous azeotropic distillation, where a completely miscible liquid separating agent is added to alter the relative volatilities; heterogeneous azeotropic distillation, where the agent, known as the entrainer, forms one or more azeotropes and causes immiscibility; distillation in the presence of ionic salts that alter the relative volatilities of the components; and pressure-swing distillation, wherein some azeotropes can be circumvented using a series of columns operating at different pressures. Residue curve maps, material balance lines, and column sequences are given for several example systems. Methods for identifying feasible separating agents are also discussed.