Why is the sky blue?

Sunlight looks white but contains every color, each traveling as a different wavelength. As it passes through the atmosphere, it collides with air molecules far smaller than the wavelengths themselves, and those collisions scatter short wavelengths, blue and violet, much more strongly than long red ones. The effect is called Rayleigh scattering, and it goes roughly as the inverse fourth power of wavelength, which is why the difference is so dramatic.

So blue light gets bounced around the whole sky and arrives at your eye from every direction, painting the dome blue. Violet scatters even more, but the sun emits less of it and our eyes are less sensitive to it, so blue wins the vote.

Sunsets are the sequel: near the horizon, light crosses far more atmosphere, the blue scatters away entirely before reaching you, and the leftover oranges and reds get the sky to themselves.