Mie scattering is scattering of light by large particles, i.e., on a larger scale than atomic and subatomic particles. It is more precisely a theory (aka Mie theory) based on the theory of electromagnetic radiation per Maxwell's equations, and the presumption of spherical particles, so when applied to non-spherical particles, it only approximates.
It scatters all wavelengths, but does have some resonances based on the size of the particle. The equations are sufficiently complicated to require numerical solution. Rayleigh scattering is, in effect, an approximation of Mie scattering for a narrower regime, i.e., particles smaller than the wavelength.
Mie scattering can be used to model the apparent color of the sky and the color of atmospheres viewed from above. It can also be used to model reddening.