The New Yorker Peggy Guggenheim (1898-1979) was the classic poor little rich girl: insecure, a woman with scores, perhaps hundreds of lovers, longing for love, the writer of tell-all memoirs. What sets her apart is that she was also the creator of one of the world’s greatest collections of modern and contemporary western art. 

Walls that are floors, floors that are walls, and stairs that go up to go down: in the brain-befuddling art of MC Escher (1898-1972) the mundane everyday meets a world of paradox in which the rules of gravity, space and material reality are thrown into disarray. From his fantastical architectural spaces with flights of stairs that lead nowhere, to dazzling tessellations that fade into infinity, Escher is synonymous with queasy optical illusions that fascinate and nauseate in equal measure.

Reputations and popularity rise and fall and rise again in cycles, and so with the redoubtable Julia Margaret Cameron (1815–1879). Now considered one of the finest photographers ever, she was an amateur gifted with incredible tenacity, intellectual and physical energy, and stamina. Stubborn and ambitious, for her class and gender she was unusually interested in business. She sold her work, which indeed she copyrighted, through the printsellers Colnaghi’s, and she was always experimenting and thinking of ways to promote her achievement.

"Exhibition on Screen" is a logical extension of the recent phenomenon of screenings of live performances of opera and theatre. Initiated with the Leonardo exhibition of 2012 at London’s National Gallery, this is its third season, and the format remains unchanged: a specific show provides the pretext for a bespoke film that goes beyond the gallery walls.

There are some wonderful things in this exhibition, and that’s no surprise: the British Empire endured for over 500 years and at its peak extended across a quarter of the world’s land mass. Preparing an exhibition of corresponding reach must have involved considering a vast range of objects, but choosing well is another matter entirely.

The strikingly architectural space that forms the upper portion of Botticini’s Palmieri altarpiece is well-suited to an entrance, forming as it does a sort of triumphal arch heralding great things beyond. And so it is that for years this painting hung over the entrance to the National Gallery’s Sainsbury Wing, oddly well-placed, but in truth of course, entirely out of place.

Tate Britain’s Duveen Galleries are currently filled with a hauntingly beautiful sound installation by Susan Philipsz (main picture). The Scottish artist won the Turner Prize in 2010 for a sound piece that didn’t really work at the Tate. Intended to be heard under the bridges spanning the River Clyde in Glasgow, the recording of Philipsz's fragile voice singing sad folk songs was largely drowned out by ambient noise.

“High Spirits” is a multi-layered title: the caricaturist Thomas Rowlandson (1757-1827) was himself a heavy gambler and a heavy drinker, continually using up his material assets in such pursuits. His high spirits extended to the Georgian society he satirised with such robust good humour; high society and even low society attracted his interests, while he also expended enormous energy detailing political and sexual intrigues.

This is Susan Hiller’s first exhibition since her Tate retrospective in 2011, and as it includes work from the 1970s to the present, it can also be seen as a retrospective of sorts. But since the selection was obviously governed by what was available for sale, it inevitably offers a piecemeal view of her achievements.

What is it about Vermeer? Just mention the name and there will be queues around the block. It’s true that there are a handful of other artists with that charisma, but none so rare as Vermeer. The Girl with a Pearl Earring is not only the subject of a recent novel and a film, but also a kind of poster for Holland as a whole, and the star of the recently reopened Mauritshaus in the Hague. At the Rijksmuseum in Amsterdam you can hardly see the handful of Vermeers for the crowds.