Microgels can be considered soft, porous and deformable particles with an internal gel structure swollen by a solvent and an average size between 100 and 1000 nm. Due to their biocompatibility, colloidal stability, their unique dynamicity and the permeability of their architecture, they are emerging as important candidates for drug delivery systems, sensing and biocatalysis. In clinical applications, the research on responsive microgels is aimed at the development of "smart" delivery systems that undergo a critical change in conformation and size in reaction to a change in environmental conditions (temperature, magnetic fields, pH, concentration gradient). Recent achievements in biodegradable polymer fabrication have resulted in new appealing strategies, including the combination of synthetic and natural-origin polymers with inorganic nanoparticles, as well as the possibility of controlling drug release remotely. In this review, we provide a literature review on the use of dual and multi-responsive chitosan-grafted-poly-(-vinylcaprolactam) (CP) microgels in drug delivery and oncological applications.