Poly(lactic acid) (PLA) is a polyester attracting growing interest every year in different application fields, such as packaging, cosmetics, food, medicine, etc. Despite its significant advantages, it has low elasticity that may hinder further development and a corresponding rise in volume of consumption. This review opens a discussion of basic approaches to PLA plasticization. These considerations include copolymerization and blending with flexible polymers, introducing oligomers and low-molecular additives, as well as structural modification. It was demonstrated that each approach has its advantages, such as simplicity and low cost, but with disadvantages, including complex processing and the need for additional reagents. According to the analysis of different approaches, it was concluded that the optimal option is the application of copolymers as the additives obtained via reactive mixing to PLA and its blends with other polymers.