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If you've ever wondered why, like Irving Berlin, you see "nothing but blue skies," you're in good company. It took many centuries and a lot of smart people -- including Aristotle, Isaac Newton, Thomas Young, James Clerk Maxwell and Hermann von Helmholtz -- to puzzle out the answer, in part because the solution encompasses so many components: the colors in sunlight, the angle at which solar illumination travels through the atmosphere, the size of airborne particles and atmospheric molecules, and the way our eyes perceive color.
Let's take the sky out of the equation for a moment and begin by looking at color. From a physics standpoint, color refers to the wavelengths of visible light leaving an object and striking a sensor, such as a human eye. These wavelengths might be reflected, or scattered, from an external source, or they might emanate from the object itself.
The color of an object changes depending on the colors contained in the light source; for example, red paint, viewed under blue light, looks black. Isaac Newton demonstrated with a prism that the white light of the sun contains all colors of the visible spectrum, so all colors are possible in sunlight.
In school, most of us learned that a banana appears yellow because it reflects yellow light and absorbs all other wavelengths. This is not accurate. A banana scatters as much orange and red as it does yellow, and scatters all of the colors of the visible range to some degree or other [source: Bohren]. The real reason it looks yellow relates to how our eyes sense light. Before we get into that, however, let's look at what color the sky actually is.

http://science.howstuffworks.com/nature/climate-weather/atmospheric/sky.htm