One cloudy afternoon this month, the line to enter the Louvre stretched around the entrance pyramid, across one long courtyard and into the next. Inside the museum, a crowd more than a dozen deep faced the Mona Lisa, most taking cellphone pictures and selfies. Near the “Winged Victory of Samothrace,” Jean-Michel Borda, visiting from Madrid, paused amid the crush. “It’s like the Métro early in the morning,” he said.

It is the height of summer, and millions of visitors are flocking to the Louvre — the busiest art museum in the world, with 9.3 million visitors last year — and to other great museums across Europe. Every year the numbers grow as new middle classes emerge, especially in Asia and Eastern Europe. Last summer the British Museum had record attendance, and for 2013 as a whole it had 6.7 million visitors, making it the world’s second-most-visited art museum, according to The Art Newspaper. Attendance at the Uffizi in Florence for the first half of the year is up almost 5 percent over last year.