Cancer is a multifactorial family of diseases that is still a leading cause of death worldwide. More than 100 different types of cancer affecting over 60 human organs are known. Chemotherapy plays a central role for treating cancer. The development of new anticancer drugs or new uses for existing drugs is an exciting and increasing research area. This is particularly important since drug resistance and side effects can limit the efficacy of the chemotherapy. Thus, there is a need for multiplexed, cost-effective, rapid, and novel screening methods that can help to elucidate the mechanism of the action of anticancer drugs and the identification of novel drug candidates. This review focuses on different label-free bioelectrochemical approaches, in particular, impedance-based methods, the solid supported membranes technique, and the DNA-based electrochemical sensor, that can be used to evaluate the effects of anticancer drugs on nucleic acids, membrane transporters, and living cells. Some relevant examples of anticancer drug interactions are presented which demonstrate the usefulness of such methods for the characterization of the mechanism of action of anticancer drugs that are targeted against various biomolecules.