High-index semiconductor nanoparticles form an alternative platform for boosting light-matter interaction at the nanoscale without plasmonic structures. Enhancement of optical response with such particles originates from excitation of their magnetic and electric Mie resonances. Here, I present our recent results on linear and nonlinear optical properties of resonant high-index particles. ​​ As an example of a linear effect, we overview the advances in enhancement of spontaneous emission with all-dielectric nanostructures. Furthermore, we have observed more than 100-fold enhancement of Raman scattering from single resonant Si nanoparticles. This observation is promising for various biological applications. ​Turning to the nonlinear side, we have developed the analytical model describing nonlinear transient response of a nanocrystalline silicon nanoparticle induced by electron-hole plasma generation. The model demonstrates the possibility of ultrafast reconfiguration of the scattering power pattern of single particles and asymmetric nanodimers, allowing for ultrafast nonlinear light routing. Our results prove the potential of silicon nanoparticles for the development of multifunctional nanoscale all-optical devices.