Cells and their derived extracellular vesicles (EVs) or exosomes contain unique molecular signatures that could be used as biomarkers for the detection of severe diseases such as cancer, as well as monitoring the treatment response. Revealing these molecular signatures requires developing non-invasive ultrasensitive tools to enable single molecule/cell-level detection using a small volume of sample with low signal-to-noise ratio background and multiplex capability. Surface-enhanced Raman scattering (SERS) can address the current limitations in studying cells and EVs through two main mechanisms: plasmon-enhanced electric field (the so-called electromagnetic mechanism (EM)), and chemical mechanism (CM). In this review, we first highlight these two SERS mechanisms and then discuss the nanomaterials that have been used to develop SERS biosensors based on each of the aforementioned mechanisms as well as the combination of these two mechanisms in order to take advantage of the synergic effect between electromagnetic enhancement and chemical enhancement. Then, we review the recent advances in designing label-aided and label-free SERS biosensors in both colloidal and planar systems to investigate the surface biomarkers on cancer cells and their derived EVs. Finally, we discuss perspectives of emerging SERS biosensors in future biomedical applications. We believe this review article will thus appeal to researchers in the field of nanobiotechnology including material sciences, biosensors, and biomedical fields.