Out of control in Byzantium
Innocent III, or a MS illuminator's idea of him
In 1201, Pope Innocent III (after spending the first three years of his pontificate trying) managed to persuade some of Europe’s lay leaders to organize yet another attempt to reclaim the Holy Land from the Muslims. They recruited an army of knights, mostly from various parts of France, but also from Flanders, Montferrat in northern Italy, and a couple of German-speaking areas in the Holy Roman Empire. The crusade’s leaders went to Venice, the most powerful of the Italian seaport states involved in the growing trade with the east. There they signed a contract with the Venetians, at a huge price, for transporting them to Egypt in two years’ time. But recruitment wasn’t a major success, and when the army assembled in Venice it was less than a third the size contracted for.

Venice had staked its whole economy on this contract, and neglected trade for over a year while building ships, assembling supplies, and training sailors to fulfill their part. The Venetians had to be paid or be ruined, and demanded the full price agreed on. But the crusaders couldn’t raise it.
Capture of Zara (painted by Tintoretto, 16th c.)
By way of compensation they agreed to help recapture the city of Zara on the Adriatic Coast (now Zadar in Croatia), which had recently revolted against Venice and transferred its allegiance to the King of Hungary, who was also the ruler of Dalmatia at that time. With the crusading army’s help, Zara was conquered and restored to Venetian rule, but this service wasn’t really sufficient to wipe out the debt, and besides, it provoked Pope Innocent into excommunicating the whole army, which he had explicitly ordered not to make war against Christians. (The picture was made in the 16th century by the Venetian painter Tintoretto as one of his many commissions by the Republic's government. Obviously the events of the Fourth Crusade had not yet become a matter for regret, at least in Venice.)

The crusade’s leader, Boniface of Montferrat, was approached by two exiled Byzantine royals, the ex-emperor Isaac II Angelos and his son Alexios. Isaac had been deposed (and blinded for good measure) by his brother, who was now Emperor Alexios III Angelos. The two exiles insisted that young Prince Alexios was the rightful emperor, loved and supported by the people of Constantinople, and they offered enormous rewards to the cash-strapped crusaders and the Venetians for taking up his cause: piles of silver, fleets of ships, hordes of soldiers, and—a boon that would hopefully calm the Pope’s wrath over attacking yet more fellow Christians—the submission of the Eastern Orthodox Church to the authority of Rome.

This offer had great appeal to the Doge of Venice, Enrico Dandolo, not only because it held out the only visible prospect of restoring the Republic’s economic health, but also because commercial relations between the Byzantine Greeks and the increasingly pushy Latins had become difficult. Not long before this, the Venetian trading community had been expelled en masse from Constantinople. They were now back in, but very uneasy about their position. Trade with the East was the foundation stone of the Venetian economy, and at this period a foothold in Constantinople was a necessary condition for it. (In addition, Dandolo, who had served on a Venetian embassy to Constantinople, seems to have had a deep personal dislike for the Byzantines.)
Enrico Dandolo, Doge of Venice 1192–1205
So the crusading army (minus some who rejected the deal and went home in disgust) sailed to Constantinople in ships full of Venetian sailors, who were also trained and accustomed to serve as soldiers. The Doge himself took the crusader’s oath and went along, though he was over 90 years old and blind. His vigor and judgment were, however, unimpaired by either of these conditions, and he was greatly respected by the crusaders. (Definite information about Dandolo's age is hard to come by, but he was reported in some accounts to have been 85 in 1192, when he became Venice’s 41st doge. I can find no information on the source of this picture, but it shows him wearing the doge’s hat, and doesn’t look like a merely conventional representation of an 85-year-old man, so perhaps it’s based on real, or at least traditional, information about how he looked.)

When the Latin forces arrived at Constantinople in June, 1203, they learned—to their apparent surprise—that Prince Alexios was not quite the people’s favorite he had claimed to be. So they besieged the city. They didn’t quite succeed in taking it, but they did breach the defenses temporarily. While inside the walls, they attempted to fend off counterattacks with a “wall of fire,” which got out of control and burned quite a bit of the city. About 20,000 people lost their homes.

A further assault scared Alexios III into running away. Prince Alexios (henceforth Alexios IV) and his father, Isaac II, were proclaimed co-emperors. The crusaders and Venetians stayed in their camp outside the city, but had free access. They were ready to collect their reward, but Alexios III had taken most of the treasury with him, and the new emperor couldn’t pay the enormous sums he had promised to the Latins. When they began to make threats, he had many of Byzantium’s treasures, including precious icons and other religious objects, melted down, but this didn’t yield enough to pay the debt, and it also cost Alexios IV whatever support he might have been able to find among the city’s people.

Street fights between Greeks and Latins became commonplace. In January of 1204, Isaac II died, and in the ensuing riot the people deposed Alexios IV. The imperial chamberlain, Alexios Doukas, had himself proclaimed Emperor Alexios V—and, lest any uncertainty linger, executed his hapless predecessor.
Final assault on Constantinople, 1204 (painted by Tintoretto, 16th c.)
The Latins, of course, demanded that the new emperor fulfill the terms of the notorious contract; the new emperor, of course, turned them down. So they decided to take the city. A full siege began in March, and the walls were breached on April 12. Another “wall of fire” tactic caused a second conflagration that destroyed even more of the city. The Venetians, whose presence was far more than ornamental, did a large share of the fighting. This picture (in which you can see the venerable Doge himself, about halfway down on the left side, encouraging his troops) is another of the celebratory paintings Tintoretto did for the Republic.

Alexios V fled, and the victorious Latins subjected Constantinople to three days of sacking. Its citizens suffered the atrocities usual on such occasions, and the city was plundered of far more than enough silver and gold to pay the crusaders’ debt to Venetians. They and the crusaders shared the very large remainder. Works of art handed down from Greek and Roman times were packed up and shipped west (for example, the four bronze horses from the Hippodrome, now to be seen on the façade of St. Mark’s Cathedral in Venice).
Geopolitical aftermath of the Fourth Crusade
The victors established a new (and fairly short-lived) Latin Empire, awarding its territories to the leaders of the crusade (those are the purple bits) and many choice islands and trading ports to Venice (the green bits). Count Baldwin of Flanders was proclaimed Emperor because Boniface of Montferrat was thought to have too many Greek connections through his relatives’ marriages to be safely granted this honor. As the map shows, the Greek empire didn’t vanish; it withdrew to Asia Minor, where it existed in two pieces separated by the Seljuk Turks, and to Epirus in northwestern Greece, where the ruling Despot was aligned with the remaining Byzantines. (Those are the orangy-reddish bits.) Later, after the southern part of the Peloponnesus had been retaken from the Principality of Achaia, another Greek-colored patch would have occupied that part of the map. It was called the Despotate of the Morea (an alternate name for the Peloponnesus).

Crete was awarded to Boniface, but he was more interested in setting up the Kingdom of Thessalonica in the generous slice of Greece that was now his. (You can guess who became its king.) So he didn't mind selling Crete to the Venetians, and only charged them 100 silver marks. (As a measure of what a silver mark was worth, the Venetians’ original price for supplying transportation and military assistance to the crusaders was 85,000 of them. The total amount of wealth stolen from Constantinople has been estimated at 900,000.)

Pope Innocent, who had up to this point perhaps deserved his name, denounced the crusaders furiously at the first news of their conquest, but later became inclined to take a more positive view of the affair. Some accounts attribute this to the generous shares of booty that arrived in Rome to adorn the Vatican and add to its coffers. Others, perhaps more accurately, explain the pope’s change of mood as based on his hope that Vatican authority over the Eastern Orthodox Church was now definitively established—Innocent was the first pope who got to appoint a Patriarch of Constantinople. But that authority lasted only as long as the Latin Empire, which the Greeks reconquered in 1261.