Krombholc is born in a musician family. He studied in Prague Conservatory in 1937-1940 and nearby Václav Talich until 1942. After, he became conductor and director of different theatres. He made various recordings of Czech operas for Supraphon, notably Janáček's Káťa Kabanová, and Martinů's Julietta. He was succeeded as chief conductor and director of the National Theatre, Prague by Václav Talich.
His wife was the soprano Maria Tauberová.
- The Gramophone Christopher Stone - 2003 "Krombholc was an outstanding Janáček conductor - his stereo Supraphon recording of Káťa Kabanová had no rivals until Decca launched its award-winning series of the five great operas under Charles Mackerras - and he rarely relaxes the tension during Jenufa's three pithy acts."
- The rough guide to opera ed Matthew Boyden, Nick Kimberley
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