Rayleigh scattering (named after the English physicist Lord Rayleigh) is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light, which may be individual atoms or molecules. It can occur when light travels in transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering is a function of the electric polarization of the particles.
Rayleigh scattering of sunlight in clear atmosphere is the main reason why the sky is blue: Rayleigh and cloud-mediated scattering contribute to diffuse light (direct light being sun-rays).
For scattering by particles similar to or larger than a wavelength, see Mie theory or discrete dipole approximation (they apply to the Rayleigh regime as well).