WHETHER you admire them or fear them, the Jesuits have a great mystique. Now that a pope has emerged from the Society of Jesus, for the first time in its five centuries of history, fascination with them is bound to grow. We can all expect to hear a lot of good and bad things about the Jesuits in the days and weeks to come. So what can be said about them for certain? They are the largest religious order within the Catholic church, with about 18,000 members, of whom 12,000 or so have undergone a long and rigorous training (at least eight years) to become priests. Since its foundation in 1540, by Ignatius of Loyola, and six of his fellow students at the university of Paris, the Society of Jesus has had a reputation for brains, energy and independence. In different ways, the Jesuits have always been at the outer edge of the Catholic world: delving deeply into foreign languages, cultures and faiths, in the ultimate hope of converting people to Christianity but in a spirit of deep and skilfully applied empathy. They brought the Christian faith to Japan, to Quebec, to the indigenous peoples of South America, always immersing themselves in the local tongue and way of life. If the Western world knows anything about China's greatest philosopher, and calls him by the Latinised name Confucius, it is because of reports sent back by the Jesuit scholar Matteo Ricci, who thought that Christianity and Confucianism were compatible. From the very start, the Jesuits were powerful and controversial. An early Jesuit mission exercised huge influence in Japan until it was suppresssed after a few decades and Christianity went underground for three centuries. The Jesuits' current leader, or superior-general, is a Spanish Japanologist, Adolfo Nicolás. Call them cultural imperialists if you like, but the Jesuits were nobody's placemen. They were spearheads for Portuguese influence in places ranging from Brazil to Goa to Macau but they didn't always endear themselves to the authorities in Lisbon; in 1759 they were expelled from the Portugese empire. In Latin America, they set up indigenous communities on the banks of the Uruguay and Paraná rivers called "reducciones". One of the stated purposes was to protect people from slavery; it was even claimed that they were bringing to life Plato's vision of an ideal republic.

And even now, the Jesuits are a challenging, contradictory bunch. They include some of Catholicism's sharpest critics of Islam, such as the Egyptian-born Samir Khalil Samir, who has urged the Vatican not to go far in its overtures to Muslims; and some of the church's most sympathetic observers of Islam, such as Thomas Michel who is an avowed admirer of the Turkish-born preacher Fethullah Gulen. A Jesuit who used to live in Syria, Paolo Dall'Oglio, has spoken out in favour of that country's armed opposition: he is the author of a book entitled "In love with Islam, Believing in Jesus". Jacques Dupuis, an influential Belgian-born Jesuit who lived mostly in India and studied Hinduism, was called to order by the Vatican for appearing to question the role of Jesus Christ as a source of absolute truth.

In the West, the Jesuits' huge prestige in the world of education has been overshadowed by child-abuse scandals. Jesuits in the northwestern United States paid out $166m to victims (mainly indigenous) of child abuse in schools. One of the order's best-known American members, the travelling preacher Donald McGuire, was exposed as a serial abuser and sent to jail for 25 years, to the acute embarrassment of senior Jesuits who had failed to respond to complaints.

Some hope that Jesuit energy and brainpower can be deployed in the struggle against child abuse. In Germany it was a Jesuit school director, Klaus Mertes, who made waves in 2010 by exposing the record of abuse at his own and many other Catholic schools.

Whether they use their knowledge responsibly or otherwise, the Jesuits are certainly privy to a lot of sensitive information. I can vouch for that. I once asked the late Miguel Arranz, a Spanish Jesuit who served as Russian interpreter to three popes, whether it was true that a senior Russian bishop, Metropolitan Nikodim of Leningrad, had died during an audience with John Paul I, the Italian pope who reigned for a few weeks in September 1978. And was it true, as rumour had it, that the Russian had dropped dead in the bewildered pope's arms? "In fact, it was my arms he dropped into," the scholar wistfully told me, before confirming that in other respects that the story was accurate.