Autumn Leaves may seem harmonically complex, especially if you've been playing a lot of three chord blues tunes, but it's actually not that tough. It might be a good exercise to learn this one in all twelve keys, and once one does a little analysis, the logic of the harmonic "skeleton" becomes clear.
The first four measures are actually in the major key presented by the key signature, simply ii - V - I and a "flip" to the IV chord in measure 4. The second set of four measures is a ii - V - I going to relative minor, best represented as vii - III - vi in the key. Melodically, just a slight variation at the conclusion of the 8 bars, 1st and 2nd endings.
An effective device on the bridge is to use a pedal tone on 5 of the relative minor for measures 17-20. Although the sheet music shows it as vii - III - vi, it could be realized as two bars of III7 "alt" (#9 b9 #5 #11) or III7 harmonic minor (b13, b9) followed by two bars on the relative minor referenced to 5 of vi. And 17-20 could also be done as 4 bars of III7alt. Once through the first four bars of the bridge it's simply a ii - V - I (in the major key) with a flip to IV at the end.
Autumn Leaves is an A A B C format. The last 8 (measures 25-32) require a little more thought than the previous 24 bars, and letter C is more closely allied to the B section than the earlier A sections. The first two measures of letter C are a ii - V in relative minor, vii - III7 of the key. Measure 24 was a IV chord, and the bass moves a tri-tone away to the vii chord in bar 25 to kick off the last 8. There's a little bit of sauce in measures 27 and 28, as the chords move from vi in bar 26 to IV in measure 29...
Once the vi (relative minor) is sounded on the first two beats of bar 27 then the next three passing chords are either realized as a descending chromatic progression bVI7 - v - bV7 or as the sequence II7 - v - I7. The IV in measure 29 is followed by vii - III in measure 30 and we arrive home on a vi6 in measure 31. Optionally, one can use a VI7 in measure 32 to turn around back to the ii chord of measure 1.
For an extreme shorthand way of thinking about Autumn Leaves: The A section is repeated and it's simply four bars in major, four in relative minor. Then the B section is four bars on V of relative minor, four bars of major. The only tricky thing is the last 8, and that's not so bad if you think of it as 8 bars in relative minor, four 2 bar chunks: vii - III, vi "passing," a IV - III7 cadence, and finally vi, the relative minor.