This may be an over simplification, but in terms of modern music or the music of the last 50 years the tritone is a dominant substitution. e.g., G7 and Db7 are, in the simplest term the same chord. The actual tritone are the same notes. That's how they relate. The 3rd and 7th of each chord are the same. All the other notes are incidental. A simple guitar blues bass line is made from this idea.
B7, E7,Bb7,Eb7,A7,D7,Ab7,Db7,G7,C7, and so forth. Play bass root plus tritone. On guitar you can visualize and hear the idea.