Spin waves (and their quasi-particle magnons) have the potential to be used as a new platform for data transfer and processing, as they can reach wavelengths in the nanometer range and frequencies in the terahertz range. However, currently, the only technique enabling the spatial investigation of the nanoscale spin waves is time-resolved x-ray microscopy, requiring synchrotron radiation and making investigation of nanoscale-related phenomena time and resource demanding. On the contrary, Brillouin light scattering (BLS) is a common tabletop technique available in many magnonics laboratories. During my PhD research, I brought the possibility of measuring nanoscale spin waves to standard micro-focused BLS setup by utilizing Mie resonances in dielectric nanoresonators. I investigated this phenomenon by measuring thermally induced spin waves in NiFe layer using a single silicon disk as a Mie resonator. To analyze the obtained data, I developed a theoretical model for micro-focused BLS. Moreover, by introducing the periodical structures, I demonstrated the measurement of the nanoscale spin waves with in-plane wavevector resolution. I measured the dispersion relation of thermally excited spin waves down to the wavelengths of 50 nm, which is one order of magnitude improvement compared to the conventional BLS. Finally, I investigated coherently excited spin waves, where the phase-resolved measurements are demonstrated by measuring the spin-wave wavelength of 204 nm with the uncertainty of only 6 nm. In summary, the presented results open a new way of analyzing the micro-focused BLS data and measuring nanoscale spin waves. The presented approach is general and can revolutionize the field of condensed matter physics and mechanobiology in the same way as a plasmon-enhanced Raman spectroscopy.