I toured with a "local" klezmer band (originally called The Crazy Klezmorim, from the San Francisco bay area) maybe 35 years ago, it was a cool tour and the players were smoking hot musicians. Many came out of the movie studio world, and had impressive credits to their names. I got the gig because an old friend of mine was involved with their label Arhoolie Records, and I had just finished a run of dates with another Arhoolie artist. Over the years I worked with many Arhoolie artists, the label's story is interesting and goes back into the early 1960's.
My original contact at Arhoolie was a guitar/mandolin player (actually multi-instrumentalist) named Dix Bruce, he was called the human jukebox, one of the most knowledgeable players about music history and arrangements that I have ever known. He played with David Grisman, and when he moved on was replaced by another good friend Joe Craven. Dix has been playing guitar, mando and banjo with the Royal Society Jazz Orchestra for probably the past 25 years or so. It's a small world, Dix played in the "all star" band at my wedding 30-something years ago.
dix bruce - YouTube
Klezmer is really a composite style of music based on eastern European blues, lots of minor key progressions, BUT if you listen closely you will hear bits of bluegrass, dixieland, European jazz, Gypsie, American blues, classical, pop, marches, cinematic music and even some rock vibe. More melody than harmony, with heavy use of counterpoint.