Periodontal diseases are worldwide health problems that negatively affect the lifestyle of many people. The long-term effect of the classical treatments, including the mechanical removal of bacterial plaque, is not effective enough, causing the scientific world to find other alternatives. Polymer–drug systems, which have different forms of presentation, chosen depending on the nature of the disease, the mode of administration, the type of polymer used, etc., have become very promising. Hydrogels, for example (in the form of films, micro-/nanoparticles, implants, inserts, etc.), contain the drug included, encapsulated, or adsorbed on the surface. Biologically active compounds can also be associated directly with the polymer chains by covalent or ionic binding (polymer–drug conjugates). Not just any polymer can be used as a support for drug combination due to the constraints imposed by the fact that the system works inside the body. Biopolymers, especially polysaccharides and their derivatives and to a lesser extent proteins, are preferred for this purpose. This paper aims to review in detail the biopolymer–drug systems that have emerged in the last decade as alternatives to the classical treatment of periodontal disease.