This paper presents a review of thermal energy storage from exhaust emissions using phase-change materials to minimize the cold-start emission from internal combustion engines. Vehicle emissions play a major role in air pollution. Efforts are being made to reduce the exhaust emissions from vehicles using catalytic converters. A catalytic converter effectively reduces the air pollutants that are produced by internal combustion engines. However, for cold engines, its efficiency decreases sharply. Therefore, for cold engines, several systems are used to maintain the temperature of the catalytic converter above its light-off temperature. Various types of arrangements are used to store thermal energy of exhaust emission using phase-change material. The performance of the catalytic converter is dependent on light-off temperature, engine working conditions, and the design of the storage unit that is embedded in it.