Detecting cancer biomarkers at an early stage at the clinical level has been the interest of numerous researchers over the years due to its impact on recovery. Therefore, attention is towards fabricating reliable, cost-effective, reproducible, and accurate devices for point-of-care screening. This review aims to highlight the emerging field of memristive biosensors and compare it to similar electrochemical devices used for cancer biomarker detection. The limit of detection (LOD) achieved by memristive biosensors was generally in the femtomolar (fM) range in comparison to field effect transistors (FET) and electrochemical immunosensors, which in most instances exhibited a LOD in the picomolar (pM) and nanomolar (nM) range. Most current memristive biosensors are fabricated using silicon nanowires, which calls for exploring different materials and structures that may lower fabrication complexity and increase reproducibility. This article examines the working principle of memristors for biosensing, the biofunctionalization of antibodies, the interaction between antibodies and antigens and its influence on memristors, as well as fabrication processes and applications of memristors for biosensing. This paper will report on memristor-based biomedical sensors focusing on cancer screening. In addition, the outlook of reduced graphene oxide (rGO) as an active material for sensing will be discussed. Memristors are anticipated to enhance the future of sensing due to their great sensitivity and simplicity of fabrication.