This fortress palace, with its crenellations and 94m-high tower, was designed by Arnolfo di Cambio between 1298 and 1314 for the signoria (city government). Today it is home to the mayor's office and the municipal council. From the top of the Torre d'Arnolfo (tower), you can revel in unforgettable views. Inside, Michelangelo's Genio della Vittoria (Spirit of Victory) sculpture graces the Salone dei Cinquecento, a magnificent painted hall created for the city's 15th-century ruling Consiglio dei Cinquecento (Council of 500).

　　During their short time in office the nine priori (consuls) – guild members picked at random – of the signoria lived in the palace. Every two months nine new names were pulled out of the hat, ensuring ample comings and goings.

　　In 1540 Cosimo I made the palace his ducal residence and centre of government, commissioning Giorgio Vasari to renovate and decorate the interior. What impresses is the 53m-long, 22m-wide Salone dei Cinquecento with swirling battle scenes, painted by Vasari and his apprentices. These glorify Florentine victories by Cosimo I over arch-rivals Pisa and Siena: unlike the Sienese, the Pisans are depicted bare of armour (play 'Spot the Leaning Tower'). To top off this unabashed celebration of his own power, Cosimo had himself portrayed as a god in the centre of the exquisite panelled ceiling – but not before commissioning Vasari to raise the original ceiling 7m in height. It took Vasari and his school, in consultation with Michelangelo, just two years (1563–65) to construct the ceiling and paint the 34 gold-leafed panels. The effect is mesmerising.

　　On the same floor, the Quartiere di Leo X ensnares the private suite of apartments of Cardinal Giovanni de' Medici (1475–1521), the son of Lorenzo Il Magnifico, who became a cardinal at the tender age of 13 and became pope in 1513 – taking the name Leo X. The Sala di Leo X is a visual celebration of his life. In the stairwell off this room, admire the wall fresco of Palazzo Vecchio during 24 June celebrations in 1558.

　　Upstairs on the 2nd floor, the Sala delle Carte Geografiche (Map Room) houses Cosimo I's fascinating collection of 16th-century maps charting everywhere in the known world at the time, from the polar regions to the Caribbean. Continue through to the private apartments of Eleonora and her ladies-in-waiting, heavy-handed decor predictably blaring the glory of the Medici. The ceiling in the Camera Verde (Green Room) by Ridolfo del Ghirlandaio was inspired by designs from Nero's Domus Aurea in Rome. The Sala dei Gigli, named after its frieze of fleur-de-lis, representing the Florentine Republic, is home to Donatello's original Judith and Holofernes.

　　On rain-free days, don't miss the 418-step hike up the palace's striking Torre d'Arnolfo, also accessible from the palace's 2nd floor. No more than 35 people are allowed at any one time and on busy days you have just 30 minutes to lap up the city panorama.