Japan has a handful of living masters coming out of their entertainment business. Westerners get told all about Hayao Miyazaki (the current God of Animation), but in terms of music we Westerners hear a lot of great stuff coming from that country without knowing who made it.
Of the most notable musicians, Yoko Kanno is the mistress whose mastery is not confined to creating classical-style film scores to rival John Williams, Hans Zimmer, and the late James Horner. This woman is the genius behind the music of Cowboy Bebop; she can, she has, and she shall continue to rock, groove, jive, wail, and croon for years to come.
She's now in her 50s. Like her colleagues of similar acumen and accomplishment, she's got a proven track record of success as well as quality. Just hit up the TV Tropes page and see what she's worked on in the anime world alone; a lot of the shows she did are emerging as classics in large part with the power of her music; take it away, and the show or film immediately weakens precipitously. (Compare how dependent Star Wars is on its music.) This is no fluke or accident; she's the Goddess of Music just as Hayao Miyazaki is the God of Animation.
Because of Yoko Kanno, we got The Seatbelts. Because of her, we got the late Origa (best known in the West for her two theme songs for Ghost in the Shell: Stand-Alone Complex). She's the one that took an ordinary pop idol track (for Macross Frontier) about a girl's love for a man and turned it into this incredible song and live performance featuring May'n and Megumi Nakajima. (Kanno's the bandleader on the keyboard.)
Yoko Kanno w/ May'n & Megumi Nakajima: "Lion" from Macross Frontier
If I ever get a chance to have something I write adapted into an anime series or feature film, I want Yoko Kanno to be in charge of the music. I think that highly of her, and once you get familiar with her body of work you'll see why I hold that opinion of her; it's rare to seem anyone who's mastered any style or genre of music, nevermind multiples, but she's done it and that achievement is to be celebrated. She's earned her accolades, and is due the respect for it. Long may you reign, Yoko Kanno.
Yoko Kanno w/ Origa (vocals): "Moon" from Turn A Gundam
(Yes, that's Kanno directing the orchestra. I told you that's she's mastered multiple styles & genres.)