In 2000, Bankside’s chief eyesore, a goliath power station—steely and cavernous, a cathedral to soulless industry—was ingeniously converted into the national contemporary art collection and is now as integral to London as the Quire of Westminster Abbey or the Dome of St Paul’s, with 5.3 million annual visitors, making it Britain’s number-two attraction. The mammoth Turbine Hall, cleared of machinery to form a meadowlike expanse of concrete, hosts works created by major-league artists in its Hyundai Commission (once called the Unilever Series). People of every background frolic there as if it were a park. This building is a star.

Maps are £1. The flow through the galleries, stacked from floors two to six on the river side of the building, is natural. Holdings focus on art made since 1900 and are divided into four loose areas of thought: On Level 2, there’s Poetry and Dream (about surrealism) plus a changing exhibition (usually £10); on Level 3, you’ll see Transformed Visions (post-war works) and another paid exhibition; on Level 4, Structure and Clarity (abstract art) and Energy and Process (arte povera, a radical movement). Descriptions too often dwell on the incestuous art world culture, something the Tate tries to ameliorate with its “Modern Art Terms” glossary smartphone app ($3), but fortunately, the pieces’ brilliance speaks louder than the curators’ self-satisfied descriptions.

The formidable collection, one of the world’s best for breadth, is always shifting, not just because the museum owns more than it can display (even in this hangar), but also because works vanish on short-term loans. Some heavy hitters never leave. My favorite: In room 6 of Transformed Visions, seven of the nine mono-tonal series created by Mark Rothko for New York City’s Four Seasons restaurant never fail to put visitors in a meditative mood (one of them, Black on Maroon, was just restored after a 2012 vandalism incident). The Tate website is updated with what’s on display either here or in the Tate Britain, which is helpful considering the facilities will be in continuous upheaval until 2016, when a 10-story southern expansion is completed.

An array of touring aids makes sense of oddity. For £4, rent a tremendous tour (one version for adults, another for kids, and you can switch between them) of the highlights on a smartphone-like video device that embellishes on the works’ meaning and context. There are four free daily guided tours, usually at 11am, noon, 2pm, and 3pm; ask at the ground-floor desk to find out where. At the family desk, open on weekends and busy days, kids pick up free drawing kits or tours based on sounds. The shop on the bottom floor is a wonderland.

The sit-down Tate Modern Restaurant on Level 6 can be inhospitable due to crowds (make a reservation: [tel] 020/7401-5103)—but there are 30 first-come bar seats facing floor-to-ceiling glass and the indelible panorama of St Paul’s and the Thames. Afternoon tea is just £15, and the fish and chips platter with mushy peas has my approval for flavor if not price (£17). You can get the same dish for £5.50 less in the cafe on the second floor, but without that stirring view. At lunch, kids under 12 eat free if a grown-up buys a main course.