Time Out says
This famous square is in the heart of the city's historic district, built on the site of the old Plaza del Arrabal, which was home to the most popular market in the late 15th century. It was Felipe II who in 1580 commissioned Juan de Herrera with the project to remodel the square, although it would be Juan Gómez de Mora who would finish the job in 1619.
The first building that was erected in Plaza Mayor as we know it today was the Casa de la Panadería bakery, designed by Diego Sillero. These days the square is the headquarters of the Madrid Tourism Centre. The equestrian statue of Felipe III in the centre of the square was designed by Giambologna and completed by Pietro Tacca in 1616.
Another important work in the area is the Arco de Cuchilleros, the most famous of the nine entrances to the square. The archway is the work of Juan Villanueva, who, after the devastating fire of 1790, decided to reduce the façades by two levels, close off the square, and raise the nine arches, so the largest in size with an enormous stairway would give passage to C/Cuchilleros.