Many therapies require the transport of therapeutic compounds or substances encapsulated in carriers that reduce or, if possible, eliminate their direct contact with healthy tissue and components of the immune system, which may react to them as something foreign and dangerous to the patient’s body. To date, inorganic nanoparticles, solid lipids, micelles and micellar aggregates, liposomes, polymeric micelles, and other polymer assemblies were tested as drug carriers. Specifically, using polymers creates a variety of options to prepare nanocarriers tailored to the chosen needs. Among polymers, aliphatic polyesters are a particularly important group. The review discusses controlled synthesis of poly(β-butyrolactone)s, polylactides, polyglycolide, poly(ε-caprolactone), and copolymers containing polymacrolactone units with double bonds suitable for preparation of functionalized nanoparticles. Discussed are syntheses of aliphatic polymers with controlled molar masses ranging from a few thousand to 106 and, in the case of polyesters with chiral centers in the chains, with controlled microstructure. The review presents also a collection of methods useful for the preparation of the drug-loaded nanocarriers: classical, developed and mastered more recently (e.g., nanoprecipitation), and forgotten but still with great potential (by the direct synthesis of the drug-loaded nanoparticles in the process comprising monomer and drug). The article describes also in-vitro and model in-vivo studies for the brain-targeted drugs based on polyester-containing nanocarriers and presents a brief update on the clinical studies and the polyester nanocarrier formulation approved for application in the clinics in South Korea for the treatment of breast, lung, and ovarian cancers.