Strictly speaking, the sky is just another feature of depth space, being an infinite backdrop against which the depth planes are set. However, it is more useful to regard it as a special case and to treat it as such. Heres an interesting fact: most skies in photographs are reasonably boring. However, most skies in paintings are either extremely interesting or very boring (exciting / boring is here measured by the amount of contrast).
There are few things capable of setting the mood of an exterior shot more powerfully than the sky. You will often find that the most effective skies are either extremely dramatic or very boring. Average skies are, by definition, neither of these. Though it can be a PITA to replace a sky entirely, effective voodoo can be had by working upon it with adjustments, masking or even augmenting it with gentle Overlays layer blends (for example: laying a more interesting sky in a light transparent layer on top of your original).
You can also darken the top of the sky and lighten a thin strip along the horizon (e.g. a Multiply and a Color Dodge blend mode). This is effectively a simple form of vignetting.
In the image pair below is an illustration of how important the sky is. The first is from the original version of Star Wars which was made before the advent of digital grading. Though the sky is not unattractive, when the film was ‘digitally remastered’ ten years later the sky was completely replaced. The new sky had a horizontal central weighting with a lessening of the relative contrast values between the foreground interest and the sky
This horizontal weighting of the sky at a point midway up the image is nothing new. Painters have been using this trick for centuries as we can see in Albert Bierstadt’s painting below: