Now that one from their own ranks has become Pope Francis, Jesuits are wondering whether there should even be a Jesuit pontiff and how former Cardinal Jorge Bergoglio can carry out this unprecedented task.
Jesuits described themselves as doubly stunned by the surprise election but sure that Francis would take his guidance from their order's long tradition of spirituality that stresses practical solutions to problems in the world.
"I am a bit shocked by the fact we have a Jesuit pope," said Vatican spokesman Rev Federico Lombardi, himself an Italian Jesuit. "Usually the Jesuits don't accept, or at least try to resist being nominated as bishops or cardinals.
"Who will the pope obey now? How will this obedience work?" asked Rev Nicolas Steeves, a French-American Jesuit doing doctoral studies in Paris.
Francis has not yet given any outline of reforms he plans for the scandal-hit Vatican, but Jesuits contacted by Reuters sketched out the guidelines they thought he would use.
SEEK GOD IN THE WORLD
"Jesuit spirituality is very practical, it's about helping people meet God in the concrete realities of their lives," said Rev Kevin O'Brien, Jesuit chaplain at Georgetown University in Washington.
"He's going to bring a change, but the first change is the change of each of our hearts," said Steeves, stressing Jesuits would look first to an inner orientation towards change and then find appropriate ways to affect it.
The Society of Jesus, the Jesuits' official name, is the largest and one of the most influential orders of the Church. It has about 18,000 priests and brothers.
It was founded in 1540 by Ignatius of Loyola, a Spanish knight who was wounded in battle and experienced a religious conversion. His military background inspired the order, which has been called "the Vatican shock troops" or "God's Marines."
It became a powerful force in Catholic education, with colleges and universities around the world, and sent zealous missionaries to far-off lands to spread the Gospel.
In the strict rules he set down, no Jesuit was to seek higher office or honors in the Church. "We take vows to waive official promotions so we're not tied down and are available to go out on mission," Steeves explained.
Only the pope can ask them to make an exception, which they do in obedience to him, he added.
TANGLING WITH THE VATICAN
That has not stopped the order from tangling with the Vatican over the centuries. In the 1980s, many of them chafed under Pope John Paul's order to stop leftist political activity linked to the liberation theology popular in Latin America then.
Some paid for their commitment with their lives. In 1989, six Jesuits teaching at the University of Central America in San Salvador were accused of being leftists during the country's civil war and were killed by the Salvadorian army.
As provincial of the Argentine Jesuits in the 1970s, Francis tried with difficulty to rein in activist priests working against the army-run dictatorship at the time, earning him accusations of being too close to the military.
The Vatican has also cracked down in Jesuit theologians and writers, including Thomas J. Reese, who resigned as editor of the Catholic magazine America in 2005 reportedly under orders from the Vatican for articles critical of Church positions.
"At least in the U.S., the Jesuits pretty much since the Second Vatican Council have collectively chosen to play the role of loyal opposition," said Russell Shaw, former spokesman for the U.S. Conference of Catholic Bishops.
BETWEEN RICH AND POOR
The contrast between the humble life Francis led in Buenos Aires, where he lived in a simple apartment rather than the comfortable archbishop's residence, and the splendor of the Vatican he now occupies reflects the tension Jesuits often experience in their work, said Rev Simon Bishop.
Jesuits learn to have special concern for the poor, but also devote much energy to education, often for the rich, said Bishop, the Jesuit chaplain at Oxford University in Britain.
"The vocation of the Jesuits is to be bridge-builders between people, those who believe and don't believe, those who are poor and those who are wealthy," he said.
"The hardest place to be is inbetween these worlds, to feel the pain of those in need and see perhaps the indifference of the others," he said. "My hope is that Francis is able to be the bridge between the poor and the corridors of power."
Rev Mark Bosco, Jesuit professor of theology and English at the Loyola University in Chicago, said Francis would probably bring to the office is the typical Jesuit approach of being active in the world rather than standing aloofly apart.
"I think he'll see the world in a positive light -- I think he'll be like John Paul II in that regard, embrace the world -- see God in all things," Bosco said.
This can express itself in different ways.
Rev Roc O'Connor, rector of the Jesuits at Creighton University in Omaha, Nebraska, said one prominent Jesuit was a speechwriter for President Richard Nixon in the 1970s while another, Daniel Berrigan, protested against the Vietnam War.
Francis's theology seems more orthodox than other Jesuits, but he takes a practical approach to the Church's problems. This different style was already reflected in the new pope's greeting at St. Peter's Square on Wednesday, said O'Brien.
"He asked for the people's blessing, he asked for silence," he said. "That's a really different approach."
His humility showed in small gestures, such as the fact he avoided wearing much of the papal finery prepared for him, said Rev Edgar Debany, an American Jesuit in Lagos now planning the first Jesuit university in Africa.
"We'll see a simplification of the liturgy," he said, noting that Benedict had brought back papal thrones, ornate vestments and a more formal style for celebrating Mass.
The choice of the papal name Francis meant the new pope would probably take inspiration from the way the 13th century reformer St Francis of Assisi, who embraced poverty as a way to reform a Church that had turned toward a more worldly life.
"What did Francis do -- he embraced the leper..." said O'Connor. "Who is the leper? Wouldn't that be an interesting thing to take on, to talk to the people popes wouldn't talk to, to the lepers of our time?"