Single-molecule (SM) surface-enhanced Raman spectroscopy (SERS) and tip-enhanced Raman spectroscopy (TERS) have emerged as analytical techniques for characterizing molecular systems in nanoscale environments. SERS and TERS use plasmonically enhanced Raman scattering to characterize the chemical information on single molecules. Additionally, TERS can image single molecules with subnanometer spatial resolution. In this review, we cover the development and history of SERS and TERS, including the concept of SERS hot spots and the plasmonic nanostructures necessary for SM detection, the past and current methodologies for verifying SMSERS, and investigations into understanding the signal heterogeneities observed with SMSERS. Moving on to TERS, we cover tip fabrication and the physical origins of the subnanometer spatial resolution. Then, we highlight recent advances of SMSERS and TERS in fields such as electrochemistry, catalysis, and SM electronics, which all benefit from the vibrational characterization of single molecules. SMSERS and TERS provide new insights on molecular behavior that would otherwise be obscured in an ensemble-averaged measurement.