Members of the board of the Metropolitan Museum of Art reportedly cried at the trustees’ meeting on Tuesday afternoon when the museum’s director of 30 years Philippe de Montebello, announced his intention to retire But once the tears are dried and the encomiums expressed, the board will have to get down to the serious task of choosing Mr. de Montebello’s successor.

The board has named a search committee led by two vice chairmen of the board, Annette de la Renta and S. Parker Gilbert, and the committee planned to hold its first meeting yesterday, according to the Met’s chairman, James Houghton, who will serve on the committee ex officio. Among their first steps will be to hire a search firm. Museums these days all use headhunters, who can take some of the burden off board members by coming up with a long list of potential candidates and doing the preliminary interviews.

At an event yesterday morning to announce Mr. de Montebello’s imminent departure, Mr. Houghton gave few clues as to what the board is looking for in a new director, other than to say that the director of the Met will have to be “a serious art scholar,” not just a skilled manager. He said that it would be a “global” search, though in responding to questions he did not seem completely familiar with the two most prominent figures from Europe — the director of the British Museum, Neil MacGregor, and the president of the Louvre, Henri Loyrette. As to whether the director will be someone who has already run a museum, Mr. Houghton said not necessarily, though it’s likely he or she would have experience running a large institution similar to a museum. One headhunter, Malcolm MacKay, of Russell Reynolds Associates, said he also thought that an art historical background was more of a non-negotiable than past experience as a director.

“The thing they will not compromise on is the art historical or curatorial background,” Mr. MacKay said. “You’ve got to be able to speak for the collection, and unless you have a serious art background, you can’t do that.” All of the candidates who have been mentioned — including, besides Mr. MacGregor and Mr. Loyrette, the director of the Art Institute of Chicago, James Cuno; the director of the Museum of Modern Art, Glenn Lowry; the director of the Fitzwilliam Museum in Cambridge, England, Timothy Potts, and the Met’s own curator of 19th-century, modern, and contemporary art, Gary Tinterow — are art historians.

The job is either the easiest or the hardest position in the museum world to fill, depending on how you look at it. Easy, because, as Mr. MacKay put it, “the Met is at the top of the ladder, internationally,” so it’s unlikely that anyone offered the job would turn it down. Hard, because it is unlikely that all of the qualities a Met director should have will be found in equal degrees in any one individual.

In addition to having scholarly credentials, the director should be a successful fund-raiser. The Met is on good financial footing, as Mr. Houghton mentioned in his remarks yesterday, but New York is a competitive fund-raising landscape, with several other major museums, in addition to institutions such as the New York Public Library, competing for donations and support.

The board will also probably look for someone who is committed to acquiring and presenting 20th-century and contemporary art. “Relative to the other departments, which are of such longer standing, [modern and contemporary art is] the department that needs the most attention,” Mr. Cuno said in an interview. Should Mr. Tinterow be chosen as the new director, it would be a sign that the board wanted the museum to engage more closely with the contemporary art world and major collectors of contemporary art. It was Mr. Tinterow who secured from the hedge-fund billionaire Steven Cohen the loan of Damien Hirst’s shark, which is now on view in the contemporary art galleries.

With the possible exception of Mr. Tinterow, however, the board is likely to choose someone who has already been a director. All of the people on the list above are currently employed, which could in a couple of cases cause some complications. Mr. Potts, for instance, just took office this month as the director of the Fitzwilliam, having previously been the director of the Kimbell Art Museum in Fort Worth, Texas. Mr. Lowry, through a spokeswoman, said that he would not take the job at the Met if offered it. (Mr. Lowry reportedly promised his new chairman, Jerry Speyer, last fall that he would stay on at MoMA for another three to five years.) Finally, as in politics, there is the likability factor. The director of the Met needs to have, as Mr. de Montebello does, the respect of 300 curators, conservators, educators, and librarians (as well as that of as an administrative staff of more than 2,000). As David Gordon, the outgoing director of the Milwaukee Art Museum, said of Mr. de Montebello: “He’s got the most incredibly strong personality: very charming, very engaging, very firm, very clear. He’s a kind of a deity among museum directors.” That won’t be easy to replace.

Mr. Houghton said yesterday that, during Mr. de Montebello’s tenure and largely thanks to his initiatives, the Met had gone from being one of the finest to being the finest museum in the world. Asked how the Met might improve, Mr. Cuno said: “To the extent to which it could [continue to be internationally pre-eminent] and also open itself up more to the community and to New York as a civic museum, that might be a challenge that one could put to it.” (Asked if he would be interested in the job, Mr. Cuno said: “I have no fantasy that that is even a prospect.”)

The director of the Nelson-Atkins Museum of Art in Kansas City, Marc Wilson, said that, even though the Met will always have a large number of visitors who are highly educated about art, it can play a leadership role, within the museum world, in exploring new ways to connect to audiences. “Philippe has done the most fantastic job of avoiding the traps of fashion,” Mr. Wilson said. But, as an industry, he said, museums have to come up with new ways of making art meaningful to “a public that is rapidly changing, and that will no longer buy into value statements of the past, [such as:] ‘Going to a museum is good for you.'”