Why is the sky blue?
Air molecules scatter short-wavelength light far more strongly than long-wavelength light, so blue arrives at your eye from every direction of the sky while red passes straight through.
Simple intuition
The plain reason, in everyday words
Sunlight looks white, but it is really every colour mixed together — you can see them separate in a rainbow. When that light comes down through the air, it bumps into the tiny molecules that make up the atmosphere. Here is the key part: the bumping does not treat all colours equally. Blue light gets knocked sideways much more easily than red light does. So blue light gets bounced around the sky in every direction, and when you look up at any random patch of sky away from the sun, the light reaching your eye from that patch is mostly the bounced blue. The red and yellow light mostly carried on in a straight line and went past you. The sky is blue because blue is the colour that gets scattered towards you from everywhere at once.
The sky is blue because it reflects the ocean.
The causation runs the other way — deep open water often looks blue partly because it reflects the sky, and partly because water itself absorbs red light. Landlocked deserts have exactly the same blue sky.
Blue light 'bounces off' air molecules like a ball off a wall.
The molecule absorbs and immediately re-emits the energy in a new direction. Nothing rebounds, and the colour dependence comes from how strongly the electron cloud is driven, not from geometry.
The sky should be violet, so the standard explanation must be wrong.
The scattering explanation is correct; it is simply incomplete without the last step. The spectrum arriving at your eye does peak towards violet, but the solar spectrum, atmospheric absorption, and the response of human cone cells together render it as blue.
The same physics sets the colour of sunsets, explains why the sky is polarised in a pattern some animals navigate by, and is the reason distant mountains look hazy blue. It is also one of the cleanest cases of a question where the physical answer and the perceptual answer are both necessary — knowing what light arrives does not tell you what colour a person sees.
Who worked it out
John Tyndall demonstrated in 1859 that small suspended particles scatter blue light preferentially. Lord Rayleigh worked out the wavelength dependence mathematically in the 1870s and showed that the molecules of the air themselves were sufficient — no dust needed.
What problem forced it
The colour of the sky was a standing puzzle in nineteenth-century physics, tangled up with the question of whether air was truly transparent and whether the atmosphere contained fine suspended matter.
How it changed since
Einstein and Smoluchowski recast the problem in terms of density fluctuations in the early twentieth century, giving the rigorous derivation. The perceptual half of the answer arrived later still, with quantitative colorimetry in the twentieth century.
Why sunsets are red
The same scattering law with one variable changed.
Why clouds are white
What happens when the scattering particles get large enough to leave the Rayleigh regime.
Written for Curio rather than collected from a forum — it is part of the curated corpus that ships with the platform. The references it draws on are listed under Sources.