"You want to give me some idea of what you're playing there?" This question was put to me in my first lesson with Mel Lewis. His greatness as a player was undeniable, but few people knew about his ability as a teacher. 
What I didn't realize at the time was that he was teaching music, not drum set. He emphasized
musicianship, history and swing, not technique. like many great masters, he knew his limitations and made the most of them. He did not have great chops but his musicality and his infallible ear were of the highest level. This was the gift he passed on to his students.   
One of Mel's greatest achievements was turning the Stan Kenton Orchestra into a swinging dynamic organization. He was nearly fired for being unable to control the band. Mel refused to play the traditional "over the top" style ala Buddy Rich. His insistent "under the table" pulse and use of dynamics changed the sound of Kenton's band.
He would also have a critical effect on Terry Gibbs Big band, but it was the band that he co-led with Thad Jones that catapulted him into the drummers hall of fame. Many drummers have filled that chair since his passing and you still hear Mel, now thats personality with a capital "P". 
If Mel had a major fault, it was that he talked and criticized too much. I and many others have always felt that it hurt his career and his standing among many major musicians. He was a very giving man who always had time to help you, if you needed it. I wish more people had known that about him. I owe him a great deal and I will never forget.

Thelonious Monk! His name is just as challenging as his music. Monks compositions have always had great melodic beauty, space and an intense rhythmic drive. 
Monk always saw drummers as a rhythmic and melodic partners.  Drummers who could swing and had a sense of composition was what he required and you had to listen. Deep!
Art Blakey wrote the book on how to play with Monk and even he had problems. You can hear Art feeling his way around on Monks early Blue Note recordings. According to Monks biographer; Robin D. G. Kelley, Monks rehearsals and record dates could be long hair raising affairs. Brilliant Corners was one of Monks best and most controversial recordings it. The title tune was 30 bars long and moving from a dirge into double time placed enormous stress on the band which included Sonny Rollins and Max Roach. The tune finally had to be assembled from 25 different takes and this was after considerable rehearsal. 
Max's drum solo on Brilliant Corners is of the best he ever recorded. His melodic sense and command of the form are remarkable. The solo would not have been possible without Max learning that thorny melody. Roy Haynes, Arthur Taylor, Frankie Dunlop and Ben Riley are among the greats who played and recorded with Monk and all of them went through the same drill. Their styles may have been different but they all learned the music and blazed the trail for the rest of us.
Playing Monks compositions has always been "big fun" for me and I know thats true for many other drummers. The feeling I get when playing his music is that he wrote it with the drums in mind and not as an afterthought
Monk always said "Learn the melody and then make a solo". Yeah!