Synthetic polymers, biopolymers, and their nanocomposites are being studied, and some of them are already used in different medical areas. Among the synthetic ones that can be mentioned are polyolefins, fluorinated polymers, polyesters, silicones, and others. Biopolymers such as polysaccharides (chitosan, hyaluronic acid, starch, cellulose, alginates) and proteins (silk, fibroin) have also become widely used and investigated for applications in medicine. Besides synthetic polymers and biopolymers, their nanocomposites, which are hybrids formed by a macromolecular matrix and a nanofiller (mineral or organic), have attracted great attention in the last decades in medicine and in other fields due to their outstanding properties. This review covers studies done recently using the polymers, biopolymers, nanocomposites, polymer micelles, nanomicelles, polymer hydrogels, nanogels, polymersomes, and liposomes used in medicine as drugs or drug carriers for cancer therapy and underlines their responses to internal and external stimuli able to make them more active and efficient. They are able to replace conventional cancer drug carriers, with better results. Appl. Sci. 2019, 9, 3899 2 of 24 nanocomposites offer numerous opportunities in diverse applications, including nanocarriers, tissue engineering, antimicrobials, sensors, etc. These new groups of materials have gained significant research interest due to their novel properties, which are gained through the addition of nanofillers. Polymer nanocomposites have significant potential in disease theranostics, and nanotechnology brings great promise in cancer drug carriers [4].Chemotherapy implies the use of drugs and, besides the drugs, carriers. Common products used as carriers include synthetic polymers, biopolymers, and polymer nanocomposites.Some of the most useful drugs for chemotherapy are toxic chemicals able to inhibit the proliferation of cancer cells. The use of chemotherapeutic drugs has been in part hindered by their poor solubility in water, their short biological half-life, their lack of targeting ability, and the development of multidrug resistance [5]. In the last decades, nanoparticles have shown significant promise as an oncology treatment modality. Responsive polymers represent a promising class of nanoparticles that can trigger delivery through the exploitation of a specific stimuli. Response to a stimulus is one of the most basic processes found in living systems. A tutorial review highlighted the recent developments in polymer-based approaches to internally responsive nanoparticles for oncology [6].One important goal of medicine is to develop carriers that can selectively deliver anticancer drugs to tumor cells with no or minimal side effects in healthy cells [7,8].Polymers and their nanocomposites in different forms, such as micelles, hydrogels, polymersomes, and liposomes, have important potential in cancer diagnosis and treatment.Nanocomposites are popular in many areas due to properties such as their unique design capacity, eco-friendly nature, ...