Resonant dielectric nanoparticles (RDNs) made of materials with large positive dielectric permittivity, such as Si, GaP, GaAs, have become a powerful platform for modern light science, enabling various fascinating applications in nanophotonics and quantum optics. In addition to light localization at the nanoscale, dielectric nanostructures provide electric and magnetic resonant responses throughout the visible and infrared spectrum, low dissipative losses and optical heating, low doping effect and absence of quenching, which are interesting 2 for spectroscopy and biosensing applications. In this review, we present state-of-the-art applications of optically resonant high-index dielectric nanostructures as a multifunctional platform for light-matter interactions. Nanoscale control of quantum emitters and applications for enhanced spectroscopy including fluorescence spectroscopy, surface-enhanced Raman scattering (SERS), biosensing, and lab-on-a-chip technology are surveyed. We describe the theoretical background underlying these effects, overview realizations of specific resonant dielectric nanostructures and hybrid excitonic systems, and outlook the challenges in this field, which remain open to future research.