Why are sunsets red and orange?

Sunlight contains all visible wavelengths. Air molecules scatter short wavelengths, the blues and violets, far more strongly than long ones, which is Rayleigh scattering and is why the daytime sky overhead is blue. At sunrise and sunset the sun sits near the horizon, so its light travels through a much longer path of atmosphere before reaching you, sometimes forty times the vertical distance. Over that path essentially all the blue is scattered out of the direct beam, leaving the long wavelengths, red and orange, to arrive.

What makes some sunsets spectacular and others plain is what else is in the air. Larger particles including dust, smoke, and pollution scatter differently and can mute colors into a hazy grey rather than intensifying them, contrary to the common belief that pollution makes better sunsets. High thin clouds are the real ingredient, because they catch the reddened light from below and spread it across the sky. Volcanic aerosols high in the stratosphere have produced famously vivid sunsets worldwide for months after major eruptions, including after Krakatoa in 1883 and Pinatubo in 1991.

Two related effects come from the same physics. The sun appears slightly flattened near the horizon because the atmosphere refracts light more strongly closer to the ground, and that refraction also means the sun you see at the moment of sunset has geometrically already set. The green flash, a brief green rim visible at the top edge of the sun under clear stable conditions, is refraction separating the colors just enough to be seen for a second or two.