Piazza della Signoria: a crime scene with a sculpture gallery in it

The square is a demolition site they never filled in

The shape of this piazza is not bad planning. It is the record of a civil war.

In the thirteenth century Florence tore itself apart between Guelphs and Ghibellines. When the Guelphs won, from 1268 onwards, they pulled down the houses of the leading Ghibelline families — above all the Uberti — and then left the ground empty. They did not sell it and they did not build on it. The vacant lot was the point: a permanent hole in the city where your enemies used to live.

It stayed rough for another century; one description calls it untidy and full of holes. It was not paved until 1385.

The tower is crooked because there is a tower inside it

Arnolfo di Cambio began the Palazzo della Signoria in 1299, on ruins of property confiscated from the same family. Rusticated pietra forte, small high windows, a crenellated gallery on corbels: a fortress that happens to be a town hall, built by a government that expected to be attacked, sometimes by its own citizens.

The Torre d'Arnolfo is 94 metres high and obviously not centred on the façade. Arnolfo built it onto an existing tower belonging to the Foraboschi family, nicknamed La Vacca — the Cow — rather than demolish it. The most recognisable silhouette in Florence is off-centre because of a building that is still in there.

Near the top are two small cells known together as the alberghetto, the little inn. Cosimo de' Medici was held there in the early 1430s before being sent into exile; he came back a year later and his family ran the city for three centuries. Girolamo Savonarola was held in the same cell in 1498, looking down at the square where he was about to be burned.

The statues are an argument about who should rule Florence

The Marzocco — a lion holding a shield with the Florentine lily. The oldest political statement here: the emblem of the republic, not of any family. By Donatello, and what stands outside is a copy.

The David — installed at the palace door in 1504 and meaning exactly what it looks like. The small one, the young one, the one with no armour, who beats the giant, placed at the door of a government that had just expelled the Medici and was surrounded by larger powers. It is a manifesto before it is a religious statue.

It stood outdoors for 369 years, until it was moved to the Galleria dell'Accademia in 1873. The copy went up in 1910.

Hercules and Cacus — by Baccio Bandinelli, put beside the David in 1534, thirty years later, after the Medici had returned. Hercules was a Medici emblem: legitimate strength, the hero who kills the thief. The returning regime installed their strongman at the same door, at the same scale, as a rebuttal. Florence has mocked it continuously ever since.

Judith and Holofernes — Donatello's bronze of a widow beheading a general. It was in the Medici family's own garden until they were expelled in 1494, when the city seized it and set it up outside the palace with an inscription about the fall of tyrants. The insult was unsubtle enough that it was eventually moved indoors.

The Fountain of Neptune — Bartolomeo Ammannati's, made for a Medici wedding in the 1560s and known to Florentines as il Biancone, the big white one. A line to the effect that Ammannati took a beautiful piece of marble and ruined it has been repeated in front of it for four hundred years.

The Loggia dei Lanzi: a gallery with no door

Built 1376–82 as a covered platform for public ceremonies and the swearing-in of officials: three wide bays of round arches on Corinthian capitals, deliberately serene against the palace's severity. The name comes from the Landsknechte — German mercenary pikemen quartered here under Cosimo I.

Inside it, Cellini's Perseus (1554), standing on the body of Medusa and holding her severed head out towards the square, commissioned by a man who had just turned a republic into a duchy. And Giambologna's Rape of the Sabine Women (1583), three figures twisting upward out of a single block of marble, composed so that there is no front — walk around it and the composition never resolves.

No door, no ticket, no queue. One of the great collections of Renaissance sculpture in the world, and you can stand in front of it at midnight in the rain.

Savonarola: four years, and then the plaque

In 1494 the French invaded Italy, the Medici were expelled, and into the vacuum stepped a Dominican friar holding no formal office who was simply the most compelling preacher anyone had heard. He told Florence it had become corrupt, vain and worldly. The city listened.

He reorganised the government around a Grand Council of five hundred citizens, and a room was built inside the palace to hold them — the Salone dei Cinquecento, about 52 metres long, one of the largest rooms in Italy, put up in 1494 by Simone del Pollaiolo, il Cronaca.

And he organised bands of children who went house to house collecting what he called vanities: mirrors, cosmetics, fine dresses, playing cards, gaming tables, musical instruments, books, works by poets. In 1497 it was piled up in this square and burned.

Within a year it had collapsed. He was excommunicated, arrested, held in the tower cell, tortured and condemned. On 23 May 1498 he was brought down with two companions. They were hanged first, and the bodies burned afterwards — an order that matters and is usually lost in the telling. The ashes were collected and thrown into the Arno, specifically so that nobody could keep a relic.

People still leave flowers on that plaque every 23 May.

The greatest commission in the history of art, and neither man finished

In 1503 the republic commissioned Leonardo da Vinci to paint a battle scene on one wall of the Salone dei Cinquecento. It then commissioned Michelangelo to paint a different battle on the facing wall.

Leonardo experimented with a technique using heat to dry the pigments, brought in braziers of hot coals, and the work ran and was ruined. Michelangelo never got past the preparatory drawing — the Pope summoned him to Rome for the Sistine Chapel — and the cartoon was eventually destroyed by the young artists who came to study it.

Sixty years later Vasari redecorated the whole hall for Cosimo I: a raised ceiling and thirty-nine painted panels about the life of one family, in a chamber built for a council of five hundred citizens.

And high on one of Vasari's own painted banners are two small words: cerca trova — seek and you shall find.

What is under the paving

When the square was lifted for repaving in the 1980s, the excavation found, in order downward: the medieval church of San Romolo; a basilica of the fifth century; Roman Florentia — baths, a theatre, and textile workshops; and below that, traces of Neolithic occupation.

Florence was finishing cloth on this exact ground a thousand years before the wool guild paid for the cathedral dome.

It was recorded, argued over, and covered back up. You are standing on a lid.

The remains of the Roman theatre under the Palazzo Vecchio can still be visited, and almost nobody does.

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How long you need

An hour, and it costs nothing. The square and the Loggia are free and always open, and late afternoon — when the sun turns the palace front gold and the crowd thins — is when the place is at its best.