Who built it and why it looks like that
It was commissioned by Pere Milà i Camps and his wife Roser Segimon, a wealthy widow whose money paid for it — the name comes from him, the funds largely from her. Older accounts give his name in its Castilian form, Pedro.
The front is the point. The façade is self-supporting stone hung on a steel frame, which means the building has no load-bearing internal walls at all: every flat could be, and still can be, rearranged freely. That is the genuinely radical thing about Casa Milà, and it is invisible from the pavement.
The ironwork on the balconies, which looks like torn seaweed, was largely the work of Josep Maria Jujol — Gaudí's collaborator and an architect in his own right, not a sculptor as older accounts describe him.
The sculpture that was never installed
The roofline was meant to carry a large religious group — a Virgin of the Rosary with attendant figures — and it is not there. Gaudí wanted it; the owners did not.
The reason was the Tragic Week of July 1909, a week of anti-clerical rioting in Barcelona in which churches and convents across the city were burnt. The Milàs, with the building half-finished, concluded that crowning it with a monumental Virgin was asking for trouble. Older accounts attribute this to riots "the year before" construction began, which puts the cause three years before the event; the riots happened in the middle of the work, and Gaudí is said to have considered abandoning the commission over it.
The roof
The best part, and the reason to time a visit for good weather. The chimneys and ventilation shafts are twisted, helmeted figures faced in stone and broken tile, set on a rolling terrace that follows the arches of the attic beneath. Barcelona nicknamed them espanta-bruixes — witch-scarers.
Beneath them, the attic is a long gallery of brick catenary arches of varying height, built as the building's laundry and insulation and now holding the Espai Gaudí, an exhibition on how he worked. The hanging chain model shown there demonstrates the method he used to calculate his leaning columns — the same technique he worked out at Colònia Güell.
One of the flats on the main floor is furnished as a bourgeois Barcelona apartment of the period, which is the only way most visitors will ever see the inside of one.
The block it stands on
Casa Milà is not the only reason to walk the Passeig de Gràcia. A few hundred metres down, one block holds three houses by the three leading architects of Modernisme, remodelled within a few years of each other in competing styles — Gaudí's Casa Batlló, Puig i Cadafalch's Casa Amatller and Domènech i Montaner's Casa Lleó Morera. Barcelona calls it the Illa de la Discòrdia, the block of discord, and it is the single densest piece of architecture in the city.
Visiting
Casa Milà has been a UNESCO World Heritage Site since 1984. It was in poor condition for much of the twentieth century and was restored after a bank bought it in 1986; it is now run by a foundation, with the upper floors open and part of the building still in other use.
Entry is by timed slot and there are several different tickets — a daytime visit, a visit at sunset or sunrise, and an evening one with a rooftop performance, which is the one worth paying extra for in summer. Exhibitions run in the main-floor galleries and change through the year. Book ahead; the queue on the pavement is long and shadeless.
Gaudí's other work is on the Antoni Gaudí page, and general practicalities on the Barcelona page.