The biggest job in education is open. Who’ll fill it?

Drew Gilpin Faust’s announcement Wednesday that she will step down next year, after 11 years of leading Harvard, has opened up the most high-profile position in higher education. Few university gigs provide as big a megaphone to address some of the most pressing issues facing higher education and society than leading the 380-year-old institution.

Faust’s tenure has largely been considered a success. But even the most accomplished have sometimes foundered at Harvard’s helm — despite the generous salary. (Faust earned $1.2 million in total compensation in 2014, the most recent year for which data is available.)

Former US Treasury secretary Summers, facing a faculty revolt, was forced to resign in 2006. Among the factors: his suggestion that women lag behind men in science and math because of innate differences between the sexes.

Rudenstine, a Renaissance literature scholar who was credited with helping to transform Princeton University, was forced to take a medical leave of absence for exhaustion after three years on the job. He was president for a decade — from 1991-2001 — and known as an aggressive fund-raiser.

“The stakes are raised, and there will be few individuals able to check all the boxes for consideration,” said Robin Mamlet, managing partner of the education practice at Witt/Kieffer, an executive search firm.

William F. Lee, senior fellow of the Harvard corporation, said in a letter to the university community Wednesday that the board would form a search committee in coming weeks.

University officials have been mum so far about their criteria and the direction in which they hope the new leader will take Harvard. Faust will step down in June 2018, so presumably her successor would arrive shortly thereafter.

But ultimately, this is Harvard, and executive search consultants and education experts said that the school can have its pick of candidates.

If Harvard goes the insider route, it will likely look to its provosts and deans. Faust, after all, was dean of the university’s Radcliffe Institute for Advanced Study before she was picked as president.

Among the possibilities from the Harvard community:

■  Alan M. Garber, provost and professor of medicine and economics, who returned to Harvard in 2011 after a long teaching stint at Stanford University. Garber earned his undergraduate degree and a doctorate in economics at Harvard. As provost, he has already been working with Faust on the school’s long-term strategy and has overseen academic planning.

■  Nitin Nohria, dean of the Harvard Business School since 2010. Nohria grew up in India and has coauthored several books on leadership. Universities have been elevating business school deans to presidents recently, said Funk, the executive search consultant, because they tend to have experience running complex schools and have networks and ties to corporate leaders and donors.

If Harvard looks outside of Cambridge for up-and-coming talent, it would be likely to seek leaders who understand large institutions and have cut their teeth at some of the top research universities. Among them:

■  David W. Leebron, the first Jewish president of Rice University when he took the helm in 2004. Under his leadership, Rice has expanded with new buildings and grown its undergraduate student body. Leebron also has a Harvard pedigree, earning his bachelor’s degree and attending law school at Harvard. He was president of the Harvard Law Review.

■  Shirley Ann Jackson, president of Rensselaer Polytechnic Institute and winner of the National Medal of Science. She was the first African-American woman to earn a doctorate at the Massachusetts Institute of Technology. Jackson has been president of RPI since 1999, and under her leadership the university has tripled its sponsorship of research awards and hired more than 325 new tenure-track faculty members.

■  Michael M. Crow, president of Arizona State University since 2002. He has increased yearly research spending, boosted the number of National Merit Scholars coming to the school, and grown the number of low-income and minority freshmen from Arizona. The university partnered with Starbucks Corp. in 2014 to offer students the chance to complete their degrees online for free.

If Harvard decides to make an unconventional pick, it has plenty of options, including:

■  B arack Obama. The former president was often accused of being too professorial — which might be a plus at Harvard. A former law school professor, he was also the first black president of the Harvard Law Review, in 1990. Obama has been busy since leaving office in January, traveling the world on the speaking circuit, defending his presidential legacy, and grabbing dinner with Canada’s prime minister, Justin Trudeau. It’s not leader of the free world — but heading one of the world’s premier universities could hold lots of appeal.

■  Janet Yellen. Her term as chair of the Federal Reserve ends in 2018, and it’s unclear whether President Trump would reappoint her or if she’d want to stay in the job. Yellen was an assistant professor at Harvard in the 1970s but spent much of her academic career at the University of California Berkeley. She wouldn’t be the first economist to lead Harvard: Lawrence Summers, the former Treasury secretary, was the 27th president of Harvard.

As Harvard launches its presidential search, all eyes are on it, and many other institutions are likely to take their cues for future leadership hunts from the university, experts said.

“It’s going to be exciting to watch,” said David Oxtoby, the president of Pomona College in California and a former president of the Harvard University Board of Overseers.

Deirdre Fernandes can be reached at deirdre.fernandes@globe.com. Follow her on Twitter @fernandesglobe. Laura Krantz can be reached at laura.krantz@globe.com.