One of the great stories in the history of the arts in Boston — right up there with the writings of the Transcendentalists or the surging ambition of the Boston Symphony Orchestra under Serge Koussevitzky — is the story of the formation of the Asian collection at the Museum of Fine Arts.

It’s great because it involved extraordinary people, because it sent out ripples of influence in every direction, and because it left behind such an impressive material legacy.

The people were, first and foremost, Edward Morse, Ernest Fenollosa, and William Sturgis Bigelow. Morse was a scientist who went to Japan in 1877 to investigate brachiopods, and then induced Fenollosa and Bigelow — an art historian and a physician, respectively — to join him there.

The three men fell in love with an idea of Old Japan, which they believed to be on the cusp of extinction. Through their acquisitions, they not only created the core of the MFA’s Asian collection, but became brilliant proselytizers on behalf of Asian art and culture generally.

Today, the MFA is famous around the world for its Asian holdings. It has a collection of Japanese art unsurpassed anywhere outside Japan.

It also has one of the best collections of Chinese paintings and sculptures in the West, one of the top three or four collections of Islamic art in the United States, and one of the largest and finest collections of Korean art outside of East Asia.

The MFA was one of the first US museums to appoint, in 1917, a curator of Indian art, Ananda Coomaraswamy, so it has built up a superlative collection in this area, too, and its collections of Vietnamese ceramics and Southeast Asian art are remarkable.

Nonetheless, for many years now, the public has been given little chance to judge the extent and quality of the museum’s Asian collections. The actual displays of Asian art have remained splintered, patchy, and irrationally organized.

Displays of Islamic art, for instance, are basically restricted to a long display case in a corridor in the west wing; this, during a period, post 9/11, which has seen interest in Islamic culture surge all over the world, and major museums such as the Louvre in Paris and the Metropolitan Museum of Art in New York respond accordingly.

Not a single gallery for Chinese art at the MFA has been renovated in 15 years — the same 15 years in which the world has watched China’s astonishing rise as a world power.

Attempts to address this unsatisfactory situation have been stymied by space restrictions, shortfalls in funding, and what some observers see as only fitful interest in Asian art on the part of the museum’s leadership.

Recent events, however, including director Malcolm Rogers’s first trip to China, in October-November, and to South Korea last March, signal a flurry of promising activity in this area.

Rogers recently appointed the highly regarded Nancy Berliner, formerly of the Peabody Essex Museum, as the new Wu Tang Curator of Chinese art. In addition, a new gallery for Japanese art — the first salvo in a larger, multi-gallery plan for Japanese art at the museum — will open Jan. 26. And the museum currently offers a fascinating exhibit surveying six centuries of Chinese lacquer, on display through Sept. 8. Most of the objects are drawn from the MFA’s collection but the show includes loans, and is complemented by a display of Chinese paintings featuring depictions of lacquer.

Rogers visited China with the museum’s head of the Art of Asia, Oceania, and Africa, Jane Portal. An expert in Korean and Chinese Art, Portal came to the MFA in 2008 from the British Museum, where she had been head of Chinese and Korean Art for more than 20 years. Her husband and grown children still reside in Britain, making family life a test; she told the Globe that the MFA’s Asian collection is the only collection for which she would have left the British Museum.

In China, Rogers and Portal attended the opening of a major exhibition of Chinese paintings at the Shanghai Museum. The MFA has lent 13 paintings to the show, including “Ladies Preparing Newly Woven Silk,” the early-12th-century Northern Song Dynasty masterpiece used on the cover of the Shanghai catalog.

In Beijing, Rogers signed a “memorandum of understanding” with Shan Jixiang, the director of the Palace Museum, also known as the Forbidden City, about future exchanges of exhibitions, object loans, and technical knowledge.

When he traveled to South Korea in March, Rogers spoke at the Korea Foundation’s Global Forum. In November, a new gallery for Korean art opened at the MFA, funded by the Korea Foundation. Adjacent to this gallery is another new gallery, for temporary exhibitions of Asian painting. This opened with an installation of 10 rare Korean Buddhist paintings from the collection, on view through June 23.

Together, the two galleries provide an elegant introduction to Korean art, and feature some breathtaking objects. Among them is a 12th-century ewer and basin set that is the most elaborate of its kind anywhere. The gold lid of the silver ewer is in the form of lotus flowers, with a phoenix perched on top.

It and a 13th-century sutra box made in lacquered wood inlaid with mother-of-pearl — one of only seven like it in the world — are wonders to behold. They are complemented by an array of refined and beautifully understated Korean ceramics in white porcelain, unglazed stoneware, and celadon, many given to the museum by renowned collector of Chinese and Korean art Charles Bain Hoyt in 1950.

Look out, too, for an 8th-century “Medicine Buddha” in gilt bronze. This was once owned by Okakura Kakuzo, author of “The Book of Tea,” and friend to such luminaries as Isabella Stewart Gardner, Martin Heidegger, Ezra Pound, and Rabindranath Tagore.

Okakura is the fourth key figure in the history of the MFA’s Asian collections. At age 18, he had acted as an interpreter for Bigelow and Fenollosa in Japan. In 1904, after holding important cultural posts in Japan, he took up an invitation to come to Boston to inspect its fast-growing Asian collection.

He became an adviser to the MFA, and later the effective head of Asian art there. He spent part of each year here and the other part in Japan, whence he brought back many objects to Boston.

Okakura’s impact is hard to overstate. According to Kojiro Tomita (1890-1976), who was curator of the Asiatic Department for 32 years, Okakura used to invite “Boston ladies from the Back Bay” to tea parties in his office.

He would ask these ladies to make silk bags to protect the Japanese lacquer objects that had lately come into the collection, and while they sewed he gave talks about Asian art. “In that way,” said Tomita, “he made more friends for the [Asian] Department and for the museum, and he was able to obtain much aid from them financially and otherwise.”

Of course, fund-raising works slightly differently today. But perhaps Okakura was onto something that has been neglected at the MFA of late — namely, generating interest in Asian art.

Too often today, the galleries showing Asian art are virtually empty of visitors. Opportunities to show off the collection’s great glories are frequently squandered, with more effort going into sending prized Asian works away than igniting interest in Asian art in the museum itself.

Right now, for instance, the show “Japanese Masterpieces From the Museum of Fine Arts, Boston” is in the midst of a four-venue tour of Japan. One of the largest touring exhibitions ever undertaken by the MFA, it was seen by more than 540,000 people at the Tokyo National Museum last spring. (To compare, a little over 110,000 people have so far seen the Mario Testino show at the MFA. It closes Feb. 3.) It then moved to Nagoya/Boston Museum of Fine Arts, the MFA’s sister institution in the city of Nagoya, and is now showing at the Kyushu National Museum, before moving to the Osaka Museum of Art in April.

According to the MFA media relations manager Amelia Kantrovitz, “The preparations for the show began more than 15 years ago; 40 MFA staff members worked on it, and more than 25,000 hours were spent on conservation.”

So, it’s a great production in every respect but one: Visitors to the MFA will not get to see it.

What a lost opportunity! The MFA is saying that many of these works will be rotated into the new permanent gallery for Japanese art when they return from Japan. But how different this is, in effect and impact, from a full-blown exhibition of the MFA’s Japanese masterpieces, accompanied by appropriate marketing and programming and colorful banners out front!

Remember, this exhibition has already been organized and assembled. After so many years of neglecting and underselling its Japanese collection, wouldn’t it be a brilliant way for the MFA to announce a new dawn — and to mark the triumphant homecoming of an extraordinary exercise in what is effectively selling coals to Newcastle? (Imagine if a Japanese museum were able to send an exhibition of stupendous American paintings from its own collection to the MFA!)

When asked why the show will not be displayed in Boston, the MFA’s response was bloodless: “Because these Japanese masterpieces have been presented on a rotating basis in our galleries, we did not consider mounting it as an exhibition.”

Instead, the museum has chosen to take a quieter, more incremental approach. It has a long-term plan that will see all the galleries for Japanese and Chinese art installed upstairs on the west side of the building, with the galleries for Korean, Indian, and Southeast Asian,

Islamic, and African and Oceanic art grouped together downstairs.

Details about the order and timing of these plans are hard to obtain. Everything depends, one is repeatedly told, on funding, which is — one is also told — easier to attract for fashionable areas like contemporary and American art than for Asian. For now, Rogers, having taken over as head of the Art of Europe department, seems more focused on overhauling the European galleries.

Still, change is happening. Along with the Korean and (soon to be opened) Japanese galleries, the MFA, late in 2011, opened a new gallery for Indian and Southeast Asian art, mostly sculptures.

This installation, overseen by curator Laura Weinstein, includes a display case for materials relating to Buddhist pilgrimages and another devoted to finds from the MFA-organized archeological digs in the Indus Valley in the 1930s.

There are also some illuminating juxtapositions of, for instance, Indian Gupta period sculpture with Cambodian Khmer sculpture, and a wonderful Javanese sculpture of a deity, more than 6 feet high and carved from volcanic rock, wearing a garland of skulls, and sporting an elaborate coif.

The installation of Japanese art opening Jan. 26 will be in the Walter Ames Compton, MD Gallery. This large room was originally designed by Francis Gardner Curtis, an important benefactor and one-time associate of the Asian department, around the time the MFA was planning its move from Copley Plaza to Huntington Avenue.

Curtis’s design was carefully based on an actual Japanese temple court in Nara. According to Anne Nishimura Morse, the museum’s senior curator of Japanese Art, the installation will include sections dedicated to the arts of the shoguns, urban art (Ukiyo-e prints, netsuke, lacquer, and so on), folk art, new acquisitions, and contemporary art.

One of the principles guiding Morse in the installation, and indeed guiding the whole Asian department, is that it should get with the times. “My predecessors,” says Morse, “felt they had to preserve a certain image of Japan.” That image, she says, was “very quaint, not dynamic like Japan is today.”

As a consequence, the plan is to include contemporary art in as many of the Asian galleries as possible, and to bridge the divide between the museum’s different departments — for example, Asian and Works on Paper, or Asian and Decorative Arts, even Asian and American — a hallmark of Rogers’s directorship.

In the meantime, the museum will host several temporary shows, either drawn from its own Asian department or brought in from elsewhere, over the next two years.

In April, “Samurai! Armor From the Ann and Gabriel Barbier-Mueller Collection,” a show from Dallas, will be installed in the Ann and Graham Gund Gallery for temporary exhibitions.

In July, a collection of 25 loose pages from Qur’ans in the MFA’s collection will be displayed in a show of calligraphy called “Sacred Pages: Conversations about the Qur’an.” Small shows of Japanese ceramics and printmaking will follow later in the year, with exhibitions of Jain art and Chinese “Bapo,” or collage-style painting, slated for 2014.

Quite a lot of activity then, and lots of ambitious plans. But how long will it be before the MFA’s plan to display its stupendous Asian collection to its full advantage is actually realized? How much backing will Jane Portal and her team of curators get from the museum’s leaders and, just as importantly, from its benefactors?

Portal believes that “museums are here to help us understand the cultures of other places.” She adds, “It sounds idealistic, but I really believe we can help with global understanding.”

There can be no doubt that, when the United States’ economic, political, and military interests are being reoriented in the direction of Asia, where almost 60 percent of the world’s population lives, and when almost 30 percent of the world’s population is Muslim, now is the time for the MFA to make the most of its tremendous assets in these areas.