History:
The history of the Jesuit order can be broken down into 3 periods: 1) the time from its
founding to its suppression by the Pope in 1773; 2) the period of suppression, 1773-1814;
3) and the restoration and its aftermath, 1814-present.
In the mid to late 18th century, the Bourbons were not only kings, many of them were also Cardinals serving in the Roman Curia, and as such they had the power to help elect a new Pope to succeed the one that had just died. Thus, when Clement XIII died in 1769, the Bourbon Cardinals were in a position to help elect a Pope whom they could easily control and who would cave in to pressure and suppress the Jesuit order. Not long after Lorenzo Ganganelli was elected Pope Clement XIV, he did indeed cave in to the pressure and agreed to suppress the order. However, he stalled for as long as possible, and formal suppression of the order was not given until 1773. That he did so unwillingly is evidenced by the fact that when Russia and Austria refused to comply with the order of suppression, he allowed the Jesuits to operate in those two countries with little or no hindrance. Elsewhere in Europe, however, the Jesuits were expelled from the universities, their lands were taken from them, and they were banned from operating as a religious order. The suppression was just as thorough elsewhere in the world, where the Pope's declaration was not needed to suppress the Jesuits. In India, where the Jesuits had established one of the largest missions, the Anglican British took over and continued their persecution of Catholics. In Japan, the Shogun was so prejudiced against them that he banned all foreigners from entering Japan under pain of death. And in the United States, which began its existence as an overwhelmingly Protestant nation, persecution of Catholics (and therefore, Jesuits) was a fact of life.
The Jesuits themselves also found ways around the Papal order of suppression by establishing other monastic orders which did not carry the Jesuit name but were decidedly similar in belief and practice. Among these were the "Fathers of Faith" and "The Society of the Sacred Heart of Jesus." After the restoration, most of the members of these groups rejoined the Jesuit order.
The popes who succeeded Clement XIV were not under the same political pressure as their predecessor because the Age of Revolution soon swept over Europe and many of the same rulers who had pushed for suppression were themselves overthrown. Thus, subsequent Popes were able to rescind many of the suppressing measures taken against the Jesuits until, in 1814, Pope Pius VII formally restored the order to its former status.
The persecution of the Jesuits was far from over. Although martyrdom was not as common as it had once been, many countries still expelled them from their universities, forced them to serve in the armed forces in time of war (which was all-too-common in the 19th century), and continued the confiscation of their property. However, they were welcomed more openly in some countries, such as Belgium, what eventually became Germany, and surprisingly, in Protestant England. And despite persecution in other countries, their numbers have continued to grow.
The survival of the Catholic Church in the young United States is almost completely due to the efforts of Bishop John Carroll of Maryland and numerous priests (among them Jesuits) that the Pope sent over from Europe. The population of lands later acquired by the U.S., such as Florida and California, was largely Catholic thanks to the efforts of Spanish Jesuit missionaries. The same holds true for large waves of Irish and German immigrants that came to America in the mid-19th century. Although the United States was still a Protestant nation, Americans were gradually being forced to accept the fact that this was just as much a land of opportunity for "those ------ Papists" as it was for any Protestant. Much of the growth of Catholicism in America can be traced to the efforts of Jesuit priests and missionaries.
Despite their heavy persecution, the role that the Jesuit order has played in the continued growth of the Catholic faith is considerable. Nowadays many Jesuits serve in parishes, especially in third-world countries and other areas plagued by poverty. There doesn't seem to be as much persecution of the Jesuit order now, especially since the Second Vatican Council. They continue to operate on the same principles set forth by St. Ignatius more than 4½ centuries ago.