Vocal training and early years
Marton was born in Budapest, where she studied voice at the Franz Liszt Academy. She made her professional debut as Kate Pinkerton in Puccini's Madama Butterfly at Hungary's Margaret Island summer festival. At the Hungarian State Opera, she made her debut as Queen of Shemaka in Rimsky-Korsakov's The Golden Cockerel in 1968. 
In 1972, she was invited by Christoph von Dohnányi to make her debut as the Countess in The Marriage of Figaro at the Frankfurt Opera. That same year, she sang Matilde in Rossini's William Tell in Florence, conducted by Riccardo Muti. She also returned to Budapest to sing Odabella in Verdi's Attila. In 1973, Marton made her debut at the Vienna State Opera in Puccini's Tosca. In 1977, she sang at the Hamburg State Opera, in the role of the Empress in Richard Strauss's Die Frau ohne Schatten, and made her San Francisco Opera debut in the title role of Verdi's Aida. In 1978, Marton made her debut at La Scala in Milan as Leonora in Verdi's Il trovatore. She debuted at the Lyric Opera of Chicago in 1979 as Maddalena in Giordano's Andrea Chénier.
In 1981, she performed at the Munich Opera Festival in the title role of Die ägyptische Helena by Richard Strauss, Wolfgang Sawallisch conducting. She sang the role of Leonore in Beethoven's Fidelio in 1982 and 1983, both performances conducted by Lorin Maazel.
In 1976, she made her Metropolitan Opera debut in New York in the role of Eva in Richard Wagner's Die Meistersinger von Nürnberg. At the Bayreuth Festival she sang both Elisabeth and Venus in Tannhäuser in 1977-1978. In 1982, Marton performed the role of Elisabeth in Tannhäuser at the Metropolitan Opera. Of that performance, The New York Times wrote:
The arrival on the scene of a fully matured Wagnerian singer is always good news, however long we must wait between dispatches from the front. The news today is that Eva Marton has arrived. The Hungarian artist, portraying Elisabeth for the first time with the Metropolitan Opera in Monday night's Tannhäuser, showed that she has the vocal and temperamental qualities to become the opera world's next important dramatic soprano. She may, in fact, already be there. The timbre is right, the sheer staying power is impressive and the instincts are those of a born actress.
Marton later became a frequent interpreter of the role of Brünnhilde in Wagner's Der Ring des Nibelungen. She performed in the complete Zubin Mehta-led Ring cycle at the Lyric Opera of Chicago in 1996. In 1998, she appeared in a new production of Lohengrin at the Hamburg State Opera, portraying Ortrud.
Marton first sang the title role of Puccini's last opera Turandot at the Vienna State Opera in 1983. It became a role with which she has been closely identified. Since 1983, she has performed the role over a hundred times including at the Metropolitan Opera, La Scala, Arena di Verona, San Francisco Opera, Lyric Opera of Chicago, Washington Opera, Opera Company of Boston under Sarah Caldwell (in 1983), Barcelona, and Houston Grand Opera. She has also portrayed Turandot in six television and video productions, including a Vienna State Opera production directed by Harold Prince, a Metropolitan Opera production created by Franco Zeffirelli production and a production designed by David Hockney filmed at the San Francisco Opera. She also sang the role at the Aurora Opera house in Gozo, Malta. She has recorded Turandot twice, conducted first by Lorin Maazel and later Roberto Abbado.
Marton's new roles in this millennium include Isolde in Wagner's Tristan und Isolde at Hamburg State Opera in 2000, and Kundry in Parsifal in Barcelona and Lisbon in 2001. In 2006 and 2007, she performed in a concert version of Giordano's Fedora at the Miskolc Opera Festival, in Elektra by Richard Strauss at the Deutsche Oper am Rhein in Düsseldorf, and in Janáček's Jenůfa in Hamburg, in the role of the Kostelnicka.  She retired from the operatic stage after performing the role of Klytemnestra in Elektra in Barcelona (Spain) in February and March 2008. However, she sang Klytämnestra in a staged performance of Elektra in Grand Théâtre de Genève in November 2010. She also keeps a small studio at the Liszt Academy of Music in Budapest, Hungary. Marton received the Persian Golden Lioness Lifetime Achievement Award in operatic music from The World Academy of Arts, Literature and Media - WAALM in 2006.