Palazzo Vecchio is the heart of Florentine civil life. Attributed to Arnolfo di Cambio and built between 1299 and 1314 to be the seat of the city's government, over the course of the centuries it has undergone a number of transformations, as the palace of the Priors, of the Signoria of the Republic, of the Grand Dukes, and as the seat of Italy's first parliament after its Unification. The oldest core, resembling a stone fortress, is distinguished by the soaring tower that overlooks the plaza below it and the whole city.

Since the early 14th century there has been a bell on the tower that tolls to mark the times of civil life, the beginning and end of the work day. The first real clock was installed on the tower in 1353 and, to verify the precision of the hour, a small sundial, not visible from the square, was placed on the tower. It served to verify the passage of the Sun at midday, making it possible to accurately reset the time indicated by the mechanical clock. Over the years, a succession of clock-makers supervised its operation, its repairs and the necessary perfecting. In the 17th century a long pendulum was added to the mechanism, hanging inside the tower from the top to the lower floors, benefiting by Galileo's intuition that the pendulum was a good regulator for a clock.

In the Palace's Hall of Lilies was placed an extraordinary planetary clock, completed in 1510 by Lorenzo della Volpaia, the founder of a dynasty of clock-makers active in Florence and Venice up to the end of the 16th century. Lorenzo was acquainted with Leonardo da Vinci, whose water meter built for Bernardo Rucellai he mentions. The clock had already disappeared by the end of the 16th century. In planetary clocks, the direct measurement of time is secondary to the aim of visualising the positions of the heavenly bodies in relation to the Earth, so as to determine with exactness the astrological influences. The construction of this type of clock required profound astronomical knowledge, accurate calculations and expertise in the field of mechanics. In 1994, based on the Notebooks of the Volpaia family, a replica of Lorenzo's lost clock was constructed, and is now displayed in the Florence Institute and Museum of the History of Science.

Palazzo Vecchio was also the site of a famous scientific experiment. In September 1657, in fact, the members of the Accademia del Cimento conducted a barometer experiment there to verify the variation in atmospheric pressure at different altitudes. The experiment was carried out by comparing the degrees measured on the same barometer at the level of Piazza della Signoria and at the top of the tower. In these two different situations, appreciable variations in the height of the column of mercury were observed, confirming what had been hypothesised by Blaise Pascal on Mount Puy de Dôme in 1648.

Inside the palace, some of the rooms evoke themes pertaining to the scientific world. One of these is the Studiolo of Francesco I, decorated with an iconographic program that shows the Grand Duke's passionate interest in the "medicinal foundry" and in alchemy, and the Hall of Geographic Charts, with characteristic decorations representing views of the city and the landscape.