Plasmonic optical biosensors for the analysis of nucleic acids have drawn a great deal of interest in nanomedicine because of their capability to overcome major limitations of conventional methods. Within this realm, surface-enhanced Raman scattering (SERS)-based sensing is progressively emerging as a powerful analytical tool beyond the basic grounds of academia to viable commercial products. SERS benefits from the synergistic combination between the intrinsic structural specificity and experimental flexibility of Raman spectroscopy, the extremely high sensitivity provided by plasmonic nanomaterials, and the tremendous advances in nanofabrication techniques and spectroscopic instrumentation. SERS application to nucleic acids analysis has been largely restricted to indirect sensing approaches, where a SERS reporter and oligonucleotide ligands are typically combined onto the nanomaterials to enable extrinsic detection of the target sequences. On the other hand, the acquisition of the intrinsic SERS vibrational fingerprint of nucleic acids (direct sensing) has traditionally suffered from major limitations. However, recent years have witnessed a burst of interest in this area, largely driven by the efforts to address key reproducibility and sensitivity issues. In this tutorial review, we summarize and discuss the most recent cutting-edge research in the field of direct SERS sensing of nucleic acids by coherently organising the diverse data reported in the literature in a structurally logical fashion.