The real story
The tower stands on soft clay, sand and silt, and began tilting within five years of its start in 1173. Wars with Genoa and Florence stopped work for almost a century, which turned out to save it: the soil had time to compress under the weight. Later builders curved the upper floors slightly to compensate, which is why the tower is subtly banana-shaped.
In 1934 Mussolini's engineers drilled holes and injected concrete into the foundation, and the tower leaned even more. It was closed in 1990 when the lean reached about 5.5 degrees. A team led by soil engineer John Burland stabilised it by stacking lead weights and then slowly extracting soil from under the high side, pulling it back about 44 cm to roughly 4 degrees. It reopened in 2001, and the team left it leaning on purpose.