The best jazz shows this month in NYC

Years ago, the big story about this Philly guitarist was his return to touring and recording after a brain aneurysm forced him to relearn guitar from scratch. These days, Martino's tale is of a veteran playing like the boy wonder he was in the late ’60s. His fretwork is its old incendiary self, and this week he's playing a series of trio-plus performances.

You may have caught altoist Shaw reeling off incisive choruses atop the rhythms of iconic drummer Roy Haynes. Catch the innovator at the helm of his own band tonight as he premieres his commission for his fellowship at the Jazz Gallery.

A powerhouse saxophonist with an unusually focused perspective, Jones seems to conjure holy ghosts and prodigal sons with every solo. His full-bodied sound is shaped as much by deep soul as by dirty funk, as he pushes the horn at both ends of its scale. Here Jones performs a politically-informed program on the eve of the November midterm elections, examining American history in the context of power and violence throughout a collection of different compositions.

This alt-jazz phenomenon made its name—and earned itself a few haters—interpreting favorites by Blondie, Nirvana and other rock icons, but has since aimed the spotlight on its striking, inventive postbop-gone-pop originals, tunes that handily demonstrate the group's uncommonly broad pool of influences. Experience the next chapter in the band's history here, with Orrin Evans taking over the piano bench in the recent absence of the idiosyncratic Ethan Iverson.

Maria Schneider has a handsome collection of Grammys, and the accolades are well deserved: This protégée of the late bandleading/arranging genius Gil Evans fronts the most polished modern jazz orchestra on the planet, a vehicle for her lush, intricate and refreshingly accessible works. Catch her at this annual Thanksgiving engagement.

The polymathic piano great and his trusty triomates (bassist Tarus Mateen and drummer Nasheet Waits) show off their slyly engaging, historically-minded modernism during a week in the Village.

Known for his distinctive tone, funky inclinations and rapport with the jam-band crowd, this inventive guitarist shows no signs of slowing down even at 66 years of age. Both his most recent albums won Grammies: 2016's Country For Old Men, which interprets classic country melodies through his signature jazz-Americana fusion, and last year's stellar collab with Jack DeJohnette and John Medeski, Hudson. Expect similarly imaginative magic from this year's Combo 66, which commemorates his most recent birthday in the title.

If you've got a taste for silky-smooth jazz fusion of the commercially viable and radio-friendly variety, then this guitarist will need no introduction. Through his music and label-building entrepreneurship, he's an architect of the smooth-jazz sound—or a chief culprit, depending upon your perspective. We recommend sampling a gig or two—pop stylings have a particular value of their own.

Before Phil Collins launched into mainstream stardom in the ‘80s peddling synth-heavy pop hits, he was a bonafide drummer's drummer—a tastefully shuffling jaw-dropping shredder who cut his teeth blowing through 10-minute improvisational jams with this innovative fusion troupe. He might not be present at this showing, but founding members John Goodsall (guitar) And Percy Jones (bass) are keeping the funk alive-and-kicking four decades on.

The vocal guitar mainstay commands a funky unit for his annual New Year's run. Last year featured chopsy veterans including Dennis Chambers, whose sticking skills earned him a spot in 2001 in the Modern Drummer Hall of Fame, so expect a similarly stellar lineup this time around.