The Borgias began the conquest of the Romagna, which became the Papal States. This conquest was more or less completed by the following pope, Julius II, who captured Bologna (he supposedly donned armor and personally directed the artillery fire, earning him his reputation as the "Warrior Pope").

Rome maintained control of Romagna for several hundred years, and it was the last region (besides Venice) to succumb to the unification around 1860, though Rome held out with a garrison of French troops. In 1870, the Franco-Prussian War began and the troops were recalled, leaving Rome open for recapture.

Since the popes had grown quite fond of their temporal powers, they were not too pleased with the unification. Pius IX declared the new state illegitimate, and called himself a "prisoner in the Vatican." For over 50 years, no acting pope would ever set foot outside it. This feud between the Italian state and the Catholic Church was the source of a major ongoing existential crisis for devout Italians, as the Vatican's policy was excommunication for any Catholic who voted in a state election.

After Mussolini came to power in 1922, he began secretly working on a treaty with Pope Pius XI (yes, they were both Piuses), which became the Lateran Accords. A major point of contention was that the pope did not want to live on Italian soil, because he could not be seen as subject to any earthly power. Mussolini agreed to the creation of an independent sovereign state in which the Pope would not be beholden to Italian politics. We call it Vatican City.

Source: Church and State in Fascist Italy, D.A. Binchy, 1970.