The detection of specific RNA molecules is a critical task for modern molecular diagnostics of infectious, oncological, and other diseases. This review provides a comprehensive analysis of the application of surface-enhanced Raman spectroscopy (SERS), a powerful technique with unique sensitivity and potential for point-of-care (POC) testing. It covers the physical principles of SERS, the types and features of nanoplasmonic substrates (Au/Ag colloids, lithographic arrays), and key strategies for RNA detection: amplification-free methods (direct detection, SERS reporter-based approaches including sandwich assays and induced aggregation) and enzyme-free amplification methods, primarily hybridization chain reaction (HCR) and catalytic hairpin assembly (CHA). Special attention is paid to progress in developing highly sensitive systems based on aptamers, which provide specific target recognition and initiation of HCR/CHA signaling cascades, as well as combinations of these methods. Key achievements in sensitivity (down to the attomolar level) and multiplexing are highlighted. The main challenges are analyzed: the need to improve substrate reproducibility, the influence of the RNA tertiary structure and protein complexes on target accessibility, optimization of affinity elements (aptamers), and integration into microfluidic platforms. It is concluded that significant progress has been made in the field of SERS-based RNA detection and emphasized that overcoming existing limitations, particularly through the use of aptamers and accounting for the native RNA structure, paves the way for creating a new generation of highly sensitive, specific, and POC-suitable diagnostic tools.