Polymer-drug conjugates are polymers with drug molecules chemically attached to polymer side chains through either a weak (degradable bond) or a dynamic covalent bond. These systems are known as pro-drugs in the inactive form when passing into the blood circulation system. When the prodrug reaches the target organ, tissue or cell, the drug is activated by cleavage of the bond between the drug and polymer, under certain conditions existing in the target organ. The advantages of polymer-drug conjugates compared to other controlled-release carriers and conventional pharmaceutical formulations are the increased drug loading capacity, prolonged in vivo; circulation time, enhanced intercellular uptake, better-controlled release, improved therapeutic efficacy, and enhanced permeability and retention effect. The aim of the present review is the investigation of polymer-drug conjugates bearing anti-cancer drugs. The polymer, through its side chains, is linked to the anti-cancer drugs via; dynamic covalent bonds, such as hydrazone/imine bonds, disulfide bonds, and boronate esters. These dynamic covalent bonds are cleaved in conditions existing only in cancer cells and not in healthy ones. Thus, ensuring the selective release of drug to the targeted tissue, reducing in this way, the frequent side effects of chemotherapy, leading to a more targeted application, despite the nature of the applied polymer, possessing the ability to aim tumors selectively via; incorporation of a relative ligand.