How do sunsets change the sky's color?

Sunsets appear red and orange for the same reason the daytime sky is blue: Rayleigh scattering. The difference is the path length of the light through the atmosphere.

• At Midday: The sun is directly overhead. Sunlight travels through the thinnest possible layer of atmosphere (relatively speaking) to reach your eyes. Only the blue and violet light is effectively scattered, making the sky blue.
• At Sunset (or Sunrise): The sun is on the horizon. To reach your eyes, its light must travel through a much thicker, denser layer of the atmosphere.

Because the light's path is so long, the blue and violet light is scattered so completely that it gets bounced away in other directions long before it ever reaches you. This "filtering" effect removes the short-wavelength colors, allowing only the longer wavelengths—the reds, oranges, and yellows—to pass straight through the thick atmosphere to your eyes.

This is why the sun itself looks red, and the clouds around it light up in brilliant orange and pink hues. You are seeing the "leftover" light that survived the long journey.