In this review, we aim to discuss the use and effect of five different drugs used in the induction of anesthesia in cancer patients. Propofol, fentanyl, rocuronium, sugammadex, and dexamethasone are commonly used to induce anesthesia and prevent pain during surgery. Currently, the mechanisms of these drugs to induce the state of anesthesia are not yet fully understood, despite their use being considered safe. An association between anesthetic agents and cancer progression has been determined; therefore, it is essential to recognize the effects of all agents during cancer treatment and to evaluate whether the treatment provided to the patients could be more precise. We also highlight the use of in silico tools to review drug interaction effects and safety, as well as the efficacy of the treatment used according to different subgroups of patients.