The first name is drawn from the patron who commissioned renowned architect Antonio Gaudi to build what became an apartment complex.
The work began in 1906, sponsored by one of Barcelona's most wealthy citizens, Pedro Milà i Camps. Initially intended to have even more obvious religious themes, anti-clerical riots from the year before motivated the owner to require that Gaudi take a more subtle approach.
The results are anything but subtle in architectural terms, both outside and in. On its completion in 1910 the local wags were so stunned, affronted or otherwise surprised they dubbed it 'The Stone Quarry' (La Pedrera).
The name is unfair.
Casa Milà is different, to be sure. But it bears no resemblance to a stone quarry, which is all sharp angles. Gaudi's creation, by contrast, is a flowing series of curves that undulate while wrapping around the corner on which the building is placed. But the theme of organic shapes doesn't stop there.
The balconies that wind around the exterior of the site are full of sea shapes. They themselves are wavelike, while the structures and objects they support integrate the same look. Wrought iron railings that resemble seaweed (the work of sculptor Josep Jujol) surround minaret-like overheads of varying heights.
The top of the building itself houses chimneys that are an outstanding continuance of the same idea. Twisting like a soft-ice cream cone, the orange stone is shaped to provide a sense of both motion and aspiration - a common theme in much of Gaudi's work. They were nicknamed espantabruxes (witch-scarers) by one of the critics of the day.
The interior elements are well matched to the building's facade and overall shape. On the ground floor is a courtyard filled with recognizable Gaudi elements: organic shapes, bright colors and lush vegetation. Summer concerts and exhibits are often held there.
One of the apartments on the top floor has been furnished in furniture and objects from the period and provides a look at what the residents might have owned. The other units are still private residences.
Higher up inside the building in the attic is a small museum/exhibition space devoted to Gaudi's work called the Espai Gaudi (Gaudi Space). Here, visitors will find numerous educational displays and photos.
There is also an unusual upside-down model of Sagrada Familia demonstrating some of the architect's structural ideas. But the space itself is also a work of art. With a glowing orange atmosphere and a hush provided by the low, curved ceiling, no visit to Casa Milà would be complete without viewing the area.
But visitors will also want not to miss the excellent rooftop. It's a delightful series of gardens laid out in the only straight lines to be found at the site, set among the unusual chimneys. It also provides a spectacular view of sunny Barcelona in the sweeping vista below.