On a cloudless day the sky is blue until the sun begins to set, when the sky grows noticeably redder. How does scattering cause this phenomenon?

The shorter violet and blue wavelengths scatter away from our field of vision. However, the longer wavelengths of light do not scatter as much and the sky becomes filled with yellow, orange and red. Red has the longest wavelength in the visible spectrum, so when the sun lies on the horizon, it appears red.