Complementary colors make a strange pair. They are opposite, yet they require each other. They incite each other to maximum vividness when together; and annihilate each other when mixed. — Johannes Itten 

Mixing Complements

As stated by Johannes Itten, complementary colors annihilate each other when mixed to create dark neutrals:

mixing orange and blue results in a neutral mixing blue and yellow results in a neutral mixing fucshia and green results in a neutral

Complementary Colors

We look at a color wheel to understand the relationships between colors. Analogous colors are positioned in such a way as to mimic the process that occurs when blending hues. The colors that are positioned opposite one another are complementary colors.

red and green yellow-green and red-purple purple and yellow

yellow-orange and blue-violet orange and blue red-orange and blue-green

To call those hues in direct opposition to each other "complements of each other" is appropriate. Complementary colors bring out the best in each other. When fully saturated complements are brought together, interesting effects are noticeable. This may be a desirable illusion, or a problem if creating visuals that are to be read.

Note that Vibrating Boundaries may occur when opposing colors are brought together.

(Notice the illusion of highlighted edges and raised text.)

Perceptual Opposites. We learn from the relationships displayed by a color wheel that every color has an opposite. Every color has both a color wheel opposite as well as a perceptual opposite. Without a color wheel, it is still possible to find the opposite of a color and this is due to a phenomenon of our eyes. Due to the physiological differences between individuals, everyone's perceptions do vary—the complements shown below are my own perceived opposites:

source >> result
blue surce - yellow after image result
sky blue surce - peach after image result
yellow surce - periwinkle after image result
orange surce - aqua after image result
green surce - mauve after image result
purple surce - lime after image result