In the last 70 years, and despite the tremendous advances in material science and engineering, and the emergence of a plethora of exciting new (often low-dimensional) materials, silicon remains the cornerstone of our modern technologies. Its electronic properties have rendered it the predominant semiconductor in electronic devices, with industry pushing towards ever smaller and faster processors. At the same time, silicon has also become a prominent material in optical communications, constituting the most common choice for waveguides and optical interconnects, allowing transmission of signals with the speed of light. But in the last 15 years, to add yet another dimension in its usefulness and versatility, new possibilities for light–matter interactions have emerged by molding silicon (and other high-refractive index dielectrics) into nanoparticles, with dimensions smaller or comparable to the wavelength of visible light. The optical response of particles with sizes of a few tens to hundreds of nm are characterised by a richness of optical modes, manifesting as the so-called Mie resonances, with both electric and magnetic character, which combine subwavelength light confinement with low losses, offering an alternative to plasmonics for nanophotonic applications. Mie-resonant systems are explored as components of optical metamaterials and metasurfaces, as efficient antennas, as building blocks for structural colouring or nanolasers, or as sensors and efficient high-quality-factor environments for manipulating light–matter interactions. Here, I will review our recent activities in understanding and tailoring the interaction of Mie-resonant particles with quantum emitters, in either the weak- or the strong-coupling regime, and our efforts to shed light on intrinsic physical mechanisms that affect the absorption and the radiation emitted by high-index dielectric particles when probed with plane waves, points dipoles, or electron beams. The diversity of interactions and optical features discussed here constitutes thus another example of exciting new physics emerging when examining known materials at different length scales.