Because of excellent thermal, mechanical, and chemical properties, poly(ethylene terephthalate) (PET) is widely used in food and beverage packaging, automotive parts, and healthcare applications. However, due to inefficient waste plastic management, these materials end up in landfills, remain in the environment for thousands of years, and threaten the ecological system. This environmental crisis has prompted the development of new upcycling processes. It is believed that chemical recycling is the way forward. In chemical recycling, PET is depolymerized into monomers using solvents. Glycolysis is the solvolytic depolymerization of PET using glycols, mainly ethylene glycol. But PET glycolysis in the absence of a catalyst is extremely slow. Several catalysts, such as metal salts and oxides, have been developed, but severe reaction conditions, low monomer yield, problems in catalyst recovery and reusability, and product purification have limited their use. Therefore, developing efficient catalysts for PET glycolysis under mild reaction conditions is the trend in PET depolymerization. In recent years, ionic liquids (ILs) and deep eutectic solvents (DESs) have emerged as new-generation materials and have shown excellent catalytic activity. Therefore, this Review focuses on the glycolysis of PET in the presence of ILs/DESs as catalysts, as studied by researchers. The effect of reaction conditions such as temperature, time, catalyst/PET ratio, and solvent/PET ratio are discussed. The processes are compared using three green metrics, energy economy coefficient (ϵ), environmental factor, and environmental energy impact factor (ξ), to find the best IL/DES. In the end, a perspective has been presented for future research in PET depolymerization.