“I want to tell you a story. About a story.” Thus spake Laurie Anderson at the beginning of her new show, Delusion, which is running for four nights as part of the Barbican’s Bite season. It was a typically cryptic, teasing prologue from a woman who, for more than 30 years, has created her own unique brand of performance art from a combination of music, poetry, stories, visual effects and electronic sounds.

Laurie Anderson's new show Delusion opens at the Barbican in London next week. Since the late 1960s she has been at the forefront of artistic innovation. From early pieces where she appeared in art galleries (wearing ice-skates in a block of ice that slowly melted), to her epic opera United States I-IV, she has carved out a niche as something between a poet, artist, technician, humourist, pop star and magician. We chatted over a coffee for breakfast in Paris last week, after I had seen Delusion the previous night.

A house of contact, a place to make contact - this bare, evocative title sits on one of Pina Bausch’s most appealing works, and also its most elastic. Brought this week to the Barbican posthumously, staged by her company on two amateur casts, Kontakthof didn’t look 32 years old, it looked both timeless and as fresh as fledglings cracking out of their egg shells.

Like Hugh Masekela, pianist Abdullah Ibrahim first emerged as a member of The Jazz Epistles - that seminal, if short-lived, group who at the start of the 1960s were the first to offer a South African take on modern jazz. Both under the stage name Dollar Brand and, following his conversion to Islam, as Abdullah Ibrahim, it's an instinct he's been honing ever since. As early influences such as Ellington and Monk have gradually become less tangible, he has emerged as one of the most distinctive artistic voices of his generation.

This week the world-renowned Tanztheater Wuppertal Pina Bausch arrives in London - for the first time, without its towering creator. Last summer the German choreographer died at the age of 68. The company intends to continue, despite the dodgy track record for troupes formed around one singular giant vision to survive long without that magnet at the core.

Sarah Kane’s last play is the stuff of legend. Since its first production some 18 months after her suicide in 1999, it’s become a favourite with black-attired drama students, nostalgic in-yer-face drama buffs and mainstream theatres all over mainland Europe. But it is rarely performed in big spaces in this country – apparently because artistic directors feel it would empty their venues. So this version, directed by Grzegorz Jarzyna of Poland’s TR Warszawa on the Barbican's main stage, is a good chance to see what we’ve been missing. Or is it?

It’s not often at a popular music concert that you hear a piece of music introduced thus: “This is a song about a ghost princess, some real birds, implied unreal birds, and a wolf boy.” But then the Magnetic Fields are a bit different from most groups; the brainchild of Stephin Merritt, a singular singer, songwriter and multi-instrumentalist from the US, they make music that’s clever, witty, strange and funny, but also thoroughly and, at times, profoundly emotional.