In a tritone substitution, the substitute chord only differs slightly from the original chord. If the original chord in a song is G7 (G, B, D, F), the tritone substitution would be Db 7 (Db, F, Ab, Cb). Note that the 3rd and 7th notes of both chords are shared in these chords (albeit with a change of role). The tritone substitution is widely used for V7 chords in the popular jazz chord progression "ii-V-I". In the key of C, this progression is "d minor, G 7, C Major". With tritone substitution, this progression would become "d minor, Db 7, C Major," which contains chromatic root movement. When performed by the bass player, this chromatic root movement creates a smooth-sounding progression.
Tonic substitutes are chords which sound very similar to the tonic chord (or I chord) in a tune. In major keys, the chords iii and vi are often substituted for the I chord, to add interest. In the key of C Major, the I Major 7 chord is "C, E, G, B" the iii chord is e minor 7 ("E, G, B, D") and the vi minor 7 chord is a minor ("A, C, E, G"). Both of the tonic substitute chords use notes from the tonic chord, which means that they will usually support a melody that was originally designed for the tonic (I) chord.
Jazz "comping" instruments (piano, guitar, organ, vibes) often use chord substitution to add harmonic interest to a jazz tune with slow harmonic change. For example, the jazz standard chord progression of "rhythm changes" uses a simple eight bar chord progression in the bridge which uses the chords III 7, VI 7, II 7, V 7; in the key of Bb, these chords are D 7, G 7, C 7, and F 7 (each for two bars). A jazz guitarist might add a "ii-V 7" aspect to each chord, which would make the progression: "a minor, D 7, d minor, G 7, g minor, C 7, c minor, F 7. Alternatively, tritone substitutions could be applied to the progression.
Theoretically, any chord can be substituted for any other chord as long as the new chord supports the melody, but in practice only a few options will sound musically and stylistically appropriate for a given song. This is a technique employed in music such as bebop or fusion to give a music piece more sophisticated harmony, or to create a new-sounding re-harmonization of an old jazz standard.
Jazz soloists and improvisers also use chord substitutions to help them add interest to their improvised solos. Jazz soloing instruments that can play chords, such as jazz guitar, piano, and organ players may use substitute chords to develop a chord solo over an existing jazz tune with slow-moving harmonies. Also, jazz improvisers may use chord substitution as a mental framework to help them create more insteresting-sounding solos. For example, a saxophonist playing an improvised solo over the basic "rhythm changes" bridge (in Bb, this is "D 7, G 7, C 7, and F 7", each for two bars) might think of a more complex progression that uses substitute chords (e.g., "a minor, D 7, d minor, G 7, g minor, C 7, c minor, F 7). In doing so, this will imply the substitute chords over the original progression, which will add interest for the listeners.
See also: Coltrane changes.