Lorin Maazel, the brilliant and mercurial American conductor whose artistic journey went from child prodigy to leader of some of the world’s top classical music institutions, died Sunday morning at his home in Castleton, Va.

His death came amid the festival he and his wife, Dietlinde Turban-Maazel, founded in 2009 to support young artists. The Castleton Festival, which announced his death, gave the official cause as complications following pneumonia.

He was 84.

Although Mr. Maazel participated in some rehearsals and coaching sessions at this summer’s festival, he also announced last month that he was canceling all his conducting engagements for next season and resigning the final year of his tenure as chief conductor of the Munich Philharmonic. His illness was not specified, but one cause appeared to be exhaustion after a grueling schedule that had him jetting from Europe to Asia to North America.

In one of his final public appearances, Mr. Maazel attended the Castleton Festival’s opening night June 28, looking frail as he gingerly made his way to a microphone, to address the audience before the opening of “Madame Butterfly” — which he was scheduled to, but did not, conduct. Instead, he spoke about the ability of opera to move past verisimilitude to something true.

Mr. Maazel had long associations with many of the world’s leading classical music institutions, including the Cleveland Orchestra, the New York Philharmonic, the Pittsburgh Symphony and the Vienna State Opera, and he made more than 350 recordings. He was the first, and youngest, American to conduct at Bayreuth, and the first to run the Vienna State Opera — though that relationship soon degenerated into a haze of political infighting that led to his departure from the post after only two years.

He was universally acknowledged to be a strong technician who had a clear beat and a photographic memory for scores. He, however, was not universally loved; in his heyday, he didn’t suffer fools lightly, and musically, he could project an air of almost clinical coolness even in glitteringly brilliant performances, as well as oddly offbeat ones.

In his later years, though, he mellowed considerably. His appointment as music director of the New York Philharmonic in 2001 was hailed by many with dread (it was announced the day after the chief critic of the New York Times wrote that such an appointment would be a disaster for the orchestra). Yet his seven-year tenure there was, if not earth-shattering, at least largely trouble-free, and the musicians remained enthusiastic about his work.

The Castleton Festival, which began in 2009 with Britten chamber operas staged in his home theater, showed him at his most generous and avuncular. Known throughout his career for demanding strikingly high fees, Mr. Maazel put quite a lot of his own money into the festival — which had a $2.5 million annual operating budget — and based it on his own 550-acre estate in Rappahannock County. The result was a significant training ground for young artists from around the world, offering both a few incandescent performances and a mom-and-pop, DIY flavor as Mr. Maazel, Dietlinde, and their three children — Orson, Leslie and Tara — essentially opened their home to the world. (Mr. Maazel is also survived by four other children from two previous marriages, Anjali Maazel, Daria Maazel Steketee, Fiona Maazel, and Ilann Maazel; and four grandchildren.)

Mr. Maazel was also a violinist — he played in the second violin section of the Pittsburgh Symphony for several years — and a composer. His opera “1984” had its world premiere at Covent Garden in 2005. On the day of his death, the Castleton Festival was scheduled to offer a concert featuring three of his works, including a setting of Shel Silverstein’s children’s book “The Giving Tree” (which Mr. Maazel performed with the National Symphony Orchestra in 2009).

Lorin Varencove Maazel was born March 5, 1930, in Neuilly-sur-Seine, France, near where his parents — singer-actor Lincoln Maazel and pianist Marie Varencove — were studying music in Paris. (Lorin Maazel’s grandfather, Isaac, was a first violinist with the Metropolitan Opera.) The family soon returned to Los Angeles, where the boy’s musical abilities became apparent. He began studying violin at age 5, and at 7 started working with Los Angeles Philharmonic associate conductor Vladimir Bakaleinikoff, whose conducting lessons became so important to Mr. Maazel that when Bakaleinikoff moved to Pittsburgh as assistant conductor with that orchestra, the Maazel family followed him.

Mr. Maazel made his formal conducting debut in 1938 (he conducted Schubert’s “Unfinished” symphony with the orchestra of the University of Idaho), and rapidly ascended to national fame by leading orchestras including the New York Philharmonic (in 1940) and Toscanini’s NBC Symphony, where he converted the initially skeptical players with, among other things, a sense of hearing that would later earn him the sobriquet of “best ears in the business.” “Little Lorin,” as he was christened in the press, became so popular that his parents had to limit his appearances to 15 a year — though, unlike many prodigies, he attended regular public school throughout his childhood.

Once Mr. Maazel hit adolescence, the child-prodigy renown melted away, and he had a few years of relative anonymity, enrolling in courses at the University of Pittsburgh (he studied languages, math and philosophy), becoming a violinist with the Pittsburgh Fine Arts Quartet and starting as a second violinist and putative apprentice conductor with the Pittsburgh Symphony Orchestra. Although mentored by Victor De Sabata and invited to make a Tanglewood debut in 1951 by Serge Koussevitzky, his conducting career was relatively stagnant until he got a Fulbright scholarship to study baroque music in Rome in 1953. That eventually led to conducting opportunities in Italy that paved the way to the Maggio Musicale in Florence, La Scala in Milan and ultimate success.

His adult career in the States lagged considerably behind his European one. Yet by 1972, he was named music director of the Cleveland Orchestra. His 10-year tenure in Cleveland, after the reign of the legendary George Szell, was controversial and ultimately, amid some high-profile tours and a catalogue of recordings, even acrimonious.

His leadership of the Pittsburgh Symphony Orchestra, from 1986 to 1996, was also uneven. During that period, he was passed over for the top spot at the Berlin Philharmonic, leading him to call a news conference to announce that he was much happier in Pittsburgh. At the same time, he was music director of the Bavarian Radio Symphony Orchestra in Munich, one of the best orchestras in Europe (where his salary drew considerable criticism in the press).

Several times in the later stages of his career, Mr. Maazel announced that he was eschewing any further music directorships to devote himself more to composing, only to have his resolution overturned by an offer he couldn’t refuse. The clearest instance of this was when the New York Philharmonic — having ditched the 73-year-old Kurt Masur because they wanted a younger conductor — came calling for Mr. Maazel, who was 71. When Mr. Maazel’s father — by then 98 and a committed New Yorker — heard that his son was taking over the Philharmonic, he said: “Now that’s a job.” (Lincoln Maazel died in 2009, at 106.)

Mr. Maazel’s kindly persona at Castleton seemed to confirm that he was becoming less forbidding with age, and more generous — in every regard — to young artists, to his community and to the audiences that got to hear some terrific performances.

“There are only two ways of growing older,” he said in an interview in 2011. “You can get more and more wrapped up in yourself, bitter and turned inward, or more mellow. The children I had whom I love challenged me to get out of my own shell. It takes life experience to shake us up.”