The early diagnosis of diseases, e.g., Parkinson’s and Alzheimer’s disease, diabetes, and various types of cancer, and monitoring the response of patients to the therapy plays a critical role in clinical treatment; therefore, there is an intensive research for the determination of many clinical analytes. In order to achieve point-of-care sensing in clinical practice, sensitive, selective, cost-effective, simple, reliable, and rapid analytical methods are required. Biosensors have become essential tools in biomarker sensing, in which electrode material and architecture play critical roles in achieving sensitive and stable detection. Carbon nanomaterials in the form of particle/dots, tube/wires, and sheets have recently become indispensable elements of biosensor platforms due to their excellent mechanical, electronic, and optical properties. This review summarizes developments in this lucrative field by presenting major biosensor types and variability of sensor platforms in biomedical applications.