In recent decades, surface-enhanced Raman spectroscopy (SERS) has become a powerful detection scheme for many applications, particularly bioassays, due to its unique strengths, such as its ultrasensitive performance. Due to the development of various SERS substrates, more SERS-based bioassays with improved sensitivity and reproducibility have been designed and manufactured. SERS is able to provide the intrinsic vibration information of molecules through the unique Raman fingerprint to enable direct detection and quantitation. Meanwhile, with the assistance of Raman-active labels, biomolecules, like proteins and nucleic acids, can be detected by the immunosandwich assay. In this review, we focus on the rational design and engineering of signal-enhancing substrates for SERS-based bioassays. Those substrates are classified into two categories, i.e., nanoparticles in colloidal suspension and nanostructures on a solid support. Each category is discussed in detail with stress on their biomedical application potential. Afterward, we summarize the SERS-based assays of proteins, nucleic acids, and viruses, for which both label-free and labeled approaches play important roles. Finally, we present the remaining challenges in the field of SERS-based bioassays and sketch out promising directions for future development.