The Tanks: Art in Action, Tate Modern, Bankside

Tate Modern just keeps growing, with bigger, wilder spaces. The buzz around the new Tanks dedicated to live and time-based art cannot be overstated: the former power station's underground oil tanks have been transformed into cavernous chambers studded with gigantic concrete pillars. Works that are usually performed on stage are given a new lease of life as the audience gets to see performers and dancers up close. The programme is an eclectic mix of old and new. Don't miss work by artist-in-residence Tania Bruguera.
• SE1, 020-7887 8888, tate.org.uk. Until 28 October. Some events ticketed. Open Sun-Thurs 10am-6pm, Fri-Sat 10am-10pm

Heatherwick Studio: Designing the Extraordinary, V&A, South Kensington

This is the first large-scale retrospective for maverick British designer and architect Thomas Heatherwick – an exploration of the creative mind behind the 2012 Olympic cauldron, the new Routemaster bus and Paddington Basin's Rolling Bridge. The magic starts with the exhibition guide – instead of a pile of folded leaflets, the guides are in massive reels of perforated paper that you roll out and tear off with an old-fashioned printer's contraption. Inspiration and invention infuse the exhibition space, with the artist's models, research materials and experiments on display.
• Cromwell Road, SW7, 020-7942 2000, vam.ac.uk. Until 30 September. Adults £6, children 12-17 £4. Open Sat-Thurs 10am-5.45pm, Fri 10am-10pm

Zabludowicz Collection Invites: Yelena Popova, Chalk Farm

The Zabludowicz Collection is housed in a former Methodist chapel, a raw set of spaces infused with all sorts of stories. This sets the tone for the intriguing experimental shows it hosts. Yelena Popova – born in Russia and based in Nottingham – has created a series of paintings, video works, text pieces and a website (discusdiscourse.com) in response to the Olympics. With dots and circles, medals and diamond shapes, the body of work is a riff on balance, harmony and movement.
• 176 Prince of Wales Road, NW5, 020-7428 8940, zabludowiczcollection.com. Until 12 August. Free. Open Thurs-Sun noon-6pm

Pursuit of Perfection: The Politics of Sport, South London Gallery, Camberwell

For a wittier, darker, more surprising take on international sporting activities, head to this show at the South London Gallery and nearby Southwark Old Town Hall which explores the political, social and media aspects of sport. Football is a particular focus as various artists deliver their own oblique reworkings of the game, be it with a stray dog sporting the hexagonal black and white markings of a football, or two women in white dresses kicking a ball around a gallery space.
• South London Gallery, 65-67 Peckham Road, SE5, Southwark Old Town Hall, 31 Peckham Road, 020-7703 6120, southlondongallery.org. Until 14 September. Free. Open Tues, Thurs-Sun 11am-6pm, Wed 11am-9pm

Deutsche Börse Photography Prize 2012, Photographers' Gallery, West End

This gallery – a haven in the heart of the city – reopened two months ago after extensive renovations. The four finalists for this award are international heavyweights working in vastly different ways: South African-born Pieter Hugo centres on a vast dumping ground for technological waste in Ghana, while British artist John Stezaker gives compelling new life to found images through collage. Rinko Kawauchi's poetic explorations of light and pattern stand in stark contrast to Christopher Williams' conceptual examinations of what photography is.
• 16-18 Ramillies Street, W1, 020-7087 9300, thephotographersgallery.org.uk. Until 9 September. Free. Open Mon-Wed, Fri, Sat 10am-6pm, Thurs 10am-8pm, Sun 11.30am-6pm