Argerich was born in Buenos Aires. Her paternal ancestors were Catalonians based in Buenos Aires since the 18th century. Her maternal grandparents were Jewish immigrants from the Russian Empire, who settled in Colonia Villa Clara in the Entre Ríos province—one of the colonies established by Baron de Hirsch and the Jewish Colonization Association. The provenance of the name Argerich is from Catalonia, Spain. She started playing the piano at age three. At the age of five, she moved to teacher Vincenzo Scaramuzza, who stressed to her the importance of lyricism and feeling. Argerich gave her debut concert in 1949 at the age of eight.
The family moved to Europe in 1955, where Argerich studied with Friedrich Gulda in Austria. Juan Perón, then the president of Argentina, made their decision possible by appointing her parents to diplomatic posts in the Argentine Embassy in Vienna. She later studied with Stefan Askenase and Maria Curcio. Argerich also seized opportunities for brief periods of coaching with Madeleine Lipatti (widow of Dinu Lipatti), Abbey Simon, and Nikita Magaloff. In 1957, at sixteen, she won both the Geneva International Music Competition and the Ferruccio Busoni International Competition, within three weeks of each other. It was at the latter that she met Arturo Benedetti Michelangeli, whom she would later seek out for lessons during a personal artistic crisis at the age of twenty, though she only had four lessons with him in a year and a half. Her greatest influence was Gulda, with whom she studied for 18 months.
Argerich rose to international prominence when she won the seventh International Chopin Piano Competition in Warsaw in 1965, at age 24. In 1965, she debuted in the United States in the Lincoln Center's Great Performers Series. In the same year, she also made her first recording, which included works by Chopin, Brahms, Ravel, Prokofiev, and Liszt, which received critical acclaim. In 1965, she recorded Chopin's Scherzo No. 3, Polonaise, Op. 53.
Argerich has often remarked in interviews of feeling "lonely" on stage during solo performances. Since the 1980s, she has staged few solo performances, concentrating instead on concertos and, in particular, chamber music, and accompanying instrumentalists in sonatas. She is noted especially for her recordings of 20th-century works by composers such as Rachmaninoff, Messiaen and Prokofiev. One notable compilation pairs Rachmaninoff's Piano Concerto No. 3 (recorded in December 1982 with the Radio Symphonie-Orchester Berlin under the direction of Riccardo Chailly) with Tchaikovsky's Piano Concerto No. 1 (February 1980, Symphonieorchester des Bayerischen Rundfunks, Kirill Kondrashin).
Argerich is also famous for her interpretation of Prokofiev's Piano Concerto No. 3, Ravel's Piano Concerto in G, and Bach's Partita No. 2 in C minor, which she has recorded several times and continues to perform.
Argerich has also promoted younger pianists, both through her annual festival and through her appearances as a member of the jury at international competitions. The pianist Ivo Pogorelić was thrust into the musical spotlight partly as a result of Argerich's actions: after he was eliminated in the third round of the 1980 International Frederic Chopin Piano Competition in Warsaw, Argerich proclaimed him a "genius" and left the jury in protest. She has supported several artists including Gabriela Montero, Mauricio Vallina, Sergio Tiempo, Gabriele Baldocci, Christopher Falzone  and others.
Argerich is president of the International Piano Academy Lake Como and performs each year at the Lugano Festival. She also created and has been General Director of the Argerich Music Festival and Encounter in Beppu, Japan, since 1996.
Her aversion to the press and publicity has resulted in her remaining out of the limelight for most of her career. Nevertheless she is widely recognized as one of the greatest pianists of her time.
Argerich has been married twice. Her first marriage, to composer-conductor Robert Chen (Chinese: 陈 亮声; pinyin: Chén Liàngshēng), and with whom she had a daughter, violinist Lyda Chen-Argerich, ended in 1964. From 1969 to 1973, Argerich was married to conductor Charles Dutoit, with whom she had a daughter, Annie Dutoit. Argerich continues to record and perform with Dutoit. She was also in a relationship with pianist Stephen Kovacevich, with whom she has a daughter, Stephanie.
In 1990, Argerich was diagnosed with malignant melanoma. After treatment, the cancer went into remission, but there was a recurrence in 1995, eventually metastasizing to her lungs and lymph nodes. Following aggressive treatment at the John Wayne Cancer Institute, which included the removal of part of her lung and use of an experimental vaccine, Argerich's cancer went into remission again. In gratitude, Argerich performed a Carnegie Hall recital benefiting the Institute. As of 2014[update][needs update], Argerich remains cancer-free. An intimate film of her life, Bloody Daughter, directed by her daughter Stephanie Argerich Blagojevic, was shown at festivals in 2013.
- The Order of the Rising Sun, Gold Rays with Rosette 2005 Japan
- Praemium Imperiale 2005 Japan
- Grammy Award for Best Instrumental Soloist(s) Performance (with orchestra):
- Grammy Award for Best Chamber Music Performance:
- Grammy Award for Best Instrumental Soloist(s) Performance (with orchestra)
- Diamond Konex Award 1999 as the most important Classical Musician of the decade in Argentina.
- Claudio Arrau Memorial Medal (1997)
- International Frédéric Chopin Piano Competition: 1st prize (1965)
- Ferruccio Busoni International Piano Competition: 1st prize (1957)
- Geneva International Music Competition: 1st prize (1957)
- Voted into Gramophone's Hall of Fame in 2012.
- Great Pianists of the 20th Century - Martha Argerich
- Great Pianists of the 20th Century - Martha Argerich II
- List of Argentines
- Ross, Alex (12 November 2001). "Madame X". The New Yorker. Retrieved 15 January 2014.
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- "La vida de una pianista única: "Martha Argerich" por Moshé Korin". Lavozylaopinion.com.ar. Retrieved 2013-10-21.
- "Portrait : Martha Argerich - Arts-Scènes". Owl-ge.ch. Retrieved 2013-10-21.
- Niel Immelman (14 April 2009). "The Guardian, 14 April 2009". London: Guardian. Retrieved 2012-01-04.
- Manildi, Donald Musician of the Year 2001 Martha Argerich, "Musical America", 2001
- Elder, Dean. Excerpts from a Rare Interview with Argerich. accessed 19 January 2010.
- "YouTube". YouTube. Retrieved 2013-10-21.
- "About". Chopin International Competition. Retrieved 17 January 2014.
- "Jury". ASU Comeptition. Retrieved 17 January 2014.
- "Ninth Competition". Arthur Rubinstein Competition. Retrieved 17 January 2014.
- Stevenson, Joseph.Allmusic Biography of Ivo Pogorelich accessed 18 January 2010
- "Progetto Martha Argerich" (in Italian). Rsi.ch. Retrieved 2012-01-04.
- "Progetto Martha Argerich" (in Italian). Rsi.ch. Retrieved 2012-01-04.
- Progetto Martha Argerich
- In a 2001 article about Martha Argerich for The New Yorker, critic Alex Ross wrote: "Argerich brings to bear qualities that are seldom contained in one person: she is a pianist of brain-teasing technical agility; she is a charismatic woman with an enigmatic reputation; she is an unaffected interpreter whose native language is music. This last may be the quality that sets her apart. A lot of pianists play huge double octaves; a lot of pianists photograph well. But few have the unerring naturalness of phrasing that allows them to embody the music rather than interpret it."
- "二十八国华人演奏家"百鸟还巢"". News.163.com. Retrieved 2012-12-11.
- "Lyda Chen-Argerich, violinist". Sens Management. Retrieved July 2, 2014.
- Hauptfuhrer, Fred; Vespa, Mary (1980-04-07). "A Top Woman Pianist, Martha Argerich, Nearly Gave Up Her Steinway for Steno". people.com. Retrieved 2014-07-02.
- Toronto Globe and Mail, concert review, March 28, 2000
- "Martha’s Bloody Daughter creates a masterpiece of intimacy and restraint". Artsjournal.com. Retrieved 2013-10-21.
- "Storia del Concorso - Fondazione Concorso Pianistico Internazionale Ferruccio Busoni". Concorsobusoni.it. Retrieved 2013-10-21.
- "Gramophone Hall of Fame : Artists Page". Gramophone.co.uk. Retrieved 11 April 2012.
- "Argerich--Discography," (August 11, 1999)
- Ross, Alex; 'Madame X', November 12, 2001, a profile of Argerich in The New Yorker
- Martha Argerich, evening talks, the award-winning documentary film about Argerich by Georges Gachot - (imdb link)
- Orga, Ates, River Plate Queen (1978, 2006), an interview with Argerich first published in the 1979 International Music Guide
- MUSIC FESTIVAL Argerich's Meeting Point in Beppu, a music festival sponsored by the Argerich Arts Foundation of Beppu, Japan
- The Martha Argerich Project
- Argerich Music news, concert schedule, articles, recordings
- Argerich's repertoire through the years
- Martha Argerich biography, CD and concert review by cosmopolis.ch
- Martha Argerich Project Brings Talent to Lugano by Euro News, June 15, 2009