Short answers, pulled from the story.
Rayleigh scattering preferentially scatters shorter wavelengths of light. Blue light has a shorter wavelength than red, so it scatters far more strongly off oxygen and nitrogen molecules, arriving at the eye from all directions across the sky. The human visual system interprets this diffuse blue and violet light as the blue color of the sky.
The phenomenon is named after Lord Rayleigh, the British physicist John William Strutt. He published foundational papers on the color and polarization of skylight in 1871, extended his analysis using James Clerk Maxwell's electromagnetic theory in 1881, and in 1899 showed that the equations applied to individual molecules, establishing the basic scientific model for the blue sky.
In 1869, John Tyndall noticed that bright light scattering off nanoscopic particulates in purified air appeared faintly blue-tinted. He guessed a similar process gave the sky its blue color, but he could not explain why blue was preferred or why atmospheric dust alone could not account for the sky's intensity. Lord Rayleigh built on and mathematically resolved Tyndall's unfinished observation.
At twilight, sunlight near the horizon travels a much longer path through the atmosphere. Blue wavelengths scatter away before reaching the eye, leaving the longer-wavelength yellows and reds on the direct line of sight. The setting Sun appears warm-colored not because it gains red light, but because the blue has been removed.
Silica optical fibers are glasses with microscopic variations in density and refractive index frozen into the material. These variations scatter light passing through the fiber, causing energy losses that follow the Rayleigh inverse fourth-power wavelength relationship. This intrinsic scattering sets a physical floor on how efficiently optical fibers can transmit signals.
Rayleigh scattering applies when particles are much smaller than the wavelength of light, specifically with a radius less than about one-tenth of the wavelength. Mie theory applies when the particle size is comparable to or larger than the wavelength. At that intermediate scale, interference effects develop across the particle's surface that the simpler Rayleigh model does not capture.