Martha Argerich is widely regarded as one of the greatest pianists of the second half of the 20th century. 

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 collaborating with 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 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.