Jazz Theory

In Jazz, we usually use 4-note seventh (7th) chords instead of 3-note triad chords. II-V progressions are really common in simple jazz. They create a sense of momentum and release; a sort of forward momentum.

Tritone substitution is a technique commonly used in Jazz. A tritone substitution is the substitution of one dominant seventh chord (possibly altered or extended) with another that is three whole steps (a tritone) from the original chord.

These chords add tension, since they aren't usually diatonic (from the central key). This tension is resolved by going down a half step to a chord that is in the key.
Adding Chord extensions is another technique to spice up the progression. Usually chords are made by stacking thirds on top of one another, which is called tertiary harmony.

We can extend chords by over-stacking thirds, without changing the basic identity of the chord. These are called 9, 11 and 13 extensions since they imply adding either the 9th, 11th or 13th note of the scale to the triad.
Non-functional harmony (or Atonal / Post-Tonal Harmony) **is also widely used in jazz. There's a whole section dedicated to this in this blog. Basically it involves the usage of chords that are completely out of key, so long as they aren't clashing with the melody.
Liberated Dissonance involves the use of polychords, mirror tones and 12-tone/serialism. All of these concepts have been given dedicated explanations in their respective sections.
Intonalism is an extreme technique in jazz, to be used sparingly. It also has its own section in this blog.