It’s impossible to think about Jean Cooke’s work without taking into account her relationship with her husband, the painter John Bratby, because his controlling personality profoundly affected every aspect of her life.

At 94, Yayoi Kusama is said to be the world’s most popular living artist. People queue for hours to spend a few minutes inside one of her Infinity Rooms, spaces with walls mirrored to create infinite reflections.

The artist Brian Clarke, surely one of the leading British artists of our time, has been all too readily dismissed as a mere craftsman. So much for being an outstanding and highly original painter who’s also done more for contemporary stained glass than any other artist in the world.

His ability to transcend boundaries and follow his own path rather than court marketable fashion and fame, has led to him being side-lined and ignored when he should be celebrated as vigorously as David Hockney and other art world giants of his generation.

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.