Carrie Mae Weems is the first live black artist to have a solo show at New York’s Guggenheim Museum, yet she is hardly known here at all. So the Barbican’s retrospective is timely, especially since, at 70, Weems is making her best work yet.

Dear Earth, Art and Hope in a Time of Crisis is a mixed show of artists who address the parlous plight of our planet. The issue obsesses me, so anyone who braves the pitfalls of exploring this difficult subject has my sympathy.

Standing just inside the door of the Whitechapel’s downstairs gallery is a luggage trolley laden with parcels (pictured below, right). This forlorn object looks as if it’s waiting to be collected, but the owner seems to have gone AWOL.The packages are labelled, not with names and addresses but descriptions of the contents, as if they had come from a museum archive.

Billed as “a journey through painting and photography”, Capturing the Moment reveals many ways in which artists have responded to photography – either by taking up the camera themselves, as did Candida Höffer, Andreas Gursky, Louise Lawler and Thomas Struth, or by making some superb paintings.

A visitor to the city wishes to gain access to the law, but a gatekeeper blocks his entrance. The man petitions this imposing figure, who is only one of a series of legal bouncers. He is told there is gate after gate. He sits, he waits, he lies down, and eventually he expires. But not before making a close study of this implacable representative of the law. He even notes the fleas in the gatekeeper’s collar.

Who created the term “electronic superhighway”? First described a system of linked communication that would become the internet? Envisioned a multichannel TV system where viewers chose for themselves what to tune into? Watch Amanda Kim’s excellent documentary Moon Is the Oldest TV and you find that the correct answer to all those questions is Nam June Paik.

One of the great things about Artangel is the interesting sites which they seek out for the artworks they commission. The latest find is the disused waiting room at Peckham Rye station, a once gracious space with a vaulted ceiling, arched windows and two fireplaces, now ripped out. The space was later converted into a billiard hall, the sign for which is still visible on the staircase wall, but when that closed down in 1962, the room was left to rot.

Isaac Julien was a student at St Martin’s School of Art when the Brixton riots broke out. Black youths took to the streets, frustrated by high rates of unemployment, police harassment, far-right intimidation and media hostility, and all hell was let loose.

In this juxtaposition of Piet Mondrian, a world famous modernist, and Hilma af Klint, a little known Swedish painter, guess who knocks your socks off ! This fascinating show is a delight and a revelation, because it declares the spiritualist underpinnings of modernism which many, until now, have sought to hide.