Hauser & Wirth, London, 13 September - 1 November 2014
London’s Hauser & Wirth presents a double-bill from this weekend, an exhibition each by contemporary artists Paul McCarthy and Pierre Huyghe. Avoid the former show if you want to keep away from abject, base subject matter – McCarthy has made his career our exposing erotic, profane and damn dirty desires, and his new paintings push all boundaries of taste imaginable… I wonder what image our picture editor is going to choose for this page? At the time of writing the content of Huyghe’s exhibition – the French conceptualist’s first in the UK since his 2006 Tate retrospective – is under wraps.

Annely Juda Fine Art, London, until 25 October 2014
I couldn’t disagree more with Jonathan Jones’s review of Anthony Caro RA’s late works in The Guardian. These sculptures on view at Annely Juda, some of the very last that the Academician produced before his death last year, honestly had me in thrall when I saw them last night, especially for the way they integrated sheets of coloured, translucent perspex with his characteristic metal shapes. The contrast between the two materials – coupled with the overall interplay of the widely various forms – amounts to a superb visual experience for the viewer, and speaks of a sculptor at the height of his powers.

National Portrait Gallery, London, until 1 March 2015
The Portrait Gallery’s new presentation of Tudor portraits is the most complete presentation of its kind to date: an essential show for anyone interested in the art or history of the period. As well as some knockout paintings (with some, like Hans Eworth’s splendid portrait of Mary I, on rare loan from other institutions), the exhibition presents, in its interpretation material, the fruits of the gallery’s five-year research project Making Art in Tudor Britain.

Whitechapel Gallery, London, until 30 November 2014
What links artists Pawel Althamer, Louise Bourgeois, Constantin Brâncusi and Willem de Kooning? The taste of Academician Mike Nelson, whose interests in art appear to be as labyrinthine as his famous installation works – if his choice of sculptures from Moscow’s V-A-C Collection, on view at the Whitechapel from this week, is anything to go by. Nelson himself fabricates an atelier-like interior inside the gallery to display his selection.

Evelyn Yard, London, until 1 November
Alex Clarke graduated from the RA Schools this summer and Evelyn Yard has wasted no time in snapping up the painter for a London solo show. The artist’s subject seems to be the very task of painting, and his fundamental feelings of doubt about it, as tentative lines or shapes of colour appear almost hesitantly on blank backgrounds, avoiding any discernable genre of practice.

Mall Galleries, London, 15 - 21 September, 2014
The charity New Lights seeks to promote artists from the North of England, bringing together established names and rising stars. In the show it stages in London’s Mall Galleries next week, Academician Norman Ackroyd will present at least eight of his highly evocative prints, which famously capture this kingdom’s coastline in all its glory.

Sam Phillips (@SamP_London) is Editor of RA Magazine.