I say living because Jean Toots Thielmans has passed away.
There are three guys that I instantly think of and then there was one I almost forgot about and have added him to the list. I refer to these guys as the Spanish guy, the Swiss guy, the French guy, and the British guy. All names in the list are active links and you can click them and check out their respective website’s or youtube videos. Wait, two of the guys don’t have websites?
All these guys have a level of technique that is indicative of hours of practice and they all have a rock solid concept of time and swing.
I am fully aware that there are other amazing players and I constantly stumble across new ones. But these are the guys that are on my radar the other ones seem to fall off the radar. Also I’m serious about the jazz designation I’m not including the blues players who dabble in swing.
Check out Julian Jackson the guy I almost forgot about: