The advent of nanotechnology, and the need to understand the chemical composition at the nanoscale, has stimulated the convergence of IR and Raman spectroscopy with scanning probe methods, resulting in new nanospectroscopy paradigms. Here we review two such methods, namely photothermal induced resonance (PTIR), also known as AFM-IR and tip-enhanced Raman spectroscopy (TERS). AFM-IR and TERS fundamentals will be reviewed in detail together with their recent crucial advances. The most recent applications, now spanning across materials science, nanotechnology, biology, medicine, geology, optics, catalysis, art conservation and other fields are also discussed. Even though AFM-IR and TERS have developed independently and have initially targeted different applications, rapid innovation in the last 5 years has pushed the performance of these, in principle spectroscopically complimentary, techniques well beyond initial expectations, thus opening new opportunities for their convergence. Therefore, subtle differences and complementarity will be highlighted together with emerging trends and opportunities.