Cancer has become one of the deadliest diseases in our society. Surgery accompanied by subsequent chemotherapy is the treatment most used to prolong or save the patient’s life. Still, it carries secondary risks such as infections and thrombosis and causes cytotoxic effects in healthy tissues. Using nanocarriers such as smart polymer micelles is a promising alternative to avoid or minimize these problems. These nanostructured systems will be able to encapsulate hydrophilic and hydrophobic drugs through modified copolymers with various functional groups such as carboxyls, amines, hydroxyls, etc. The release of the drug occurs due to the structural degradation of these copolymers when they are subjected to endogenous (pH, redox reactions, and enzymatic activity) and exogenous (temperature, ultrasound, light, magnetic and electric field) stimuli. We did a systematic review of the efficacy of smart polymeric micelles as nanocarriers for anticancer drugs (doxorubicin, paclitaxel, docetaxel, lapatinib, cisplatin, adriamycin, and curcumin). For this reason, we evaluate the influence of the synthesis methods and the physicochemical properties of these systems that subsequently allow an effective encapsulation and release of the drug. On the other hand, we demonstrate how computational chemistry will enable us to guide and optimize the design of these micelles to carry out better experimental work.