The size parameter q = 2πR/λ in spheres with a radius R = (2–3)λ (λ is the radiation wavelength) is on the order of 10. Strong Mie resonances ( $$\ell \geqslant 5$$ ) are observed in these structures; these resonances lead to peculiar optical phenomena, caused by the interference of high-order multipoles and localization of magnetic fields. Examples of such optical phenomena are presented in this review.