Leopold Ludwig was a leading Austrian conductor. Particularly well known as an opera conductor, he was also one of the first to make stereo LP recordings of symphonies of Gustav Mahler.

He learned piano as a boy and continued to study the instrument at the Vienna Conservatory with Emil Pauer. He began his conducting career in the traditional German manner, working himself up through a number of coaching and then conducting positions in provincial opera houses in south Germany and in Brno, Czechoslovakia.

He became the Music Director of the Oldenburg Staatsoper (State Opera) in 1936. Frequent guest conducting appearances in Berlin brought him to national attention, leading to his appointment as Principal Conductor of the Vienna Staatsoper in 1939. He became Principal Conductor of the Berlin Städtische Oper in 1943. After the war he continued in that position until 1951, and also frequently conducted at the Berlin Staatsoper. ("Städtische" means "Municipal"; the prefix "Staats-" means "State." The Berlin Städtische Oper is now the Deutsche Opera Berlin.)

In 1950, Ludwig was appointed General Music Director of the Hamburg Staatsoper, effective 1951. This was the base for his expanding international reputation, and he remained there until 1971. He was an active and effective administrator, and improved its artistic and musical standards. In 1952, he took it on an important festival visit, to the Edinburgh Festival in the United Kingdom, beginning a practice of taking to major foreign venues and festivals. (Another of the company's most important overseas visits was to the Lincoln Center Festival in New York in 1967). He also modernized and broadened the company's repertory.

He also made notable guest conducting appearances. He debuted in the United States at the San Francisco Opera in 1958, frequently returning there through 1968. He led the Glyndebourne (England) Festival Opera's first production of Richard Strauss' Der Rosenkavalier in 1959. He championed Paul Hindemith's opera Mathis der Maler in a series of performances in 1967, though a series of cuts he made in it were considered questionable. His first appearance with the Metropolitan Opera House in New York was in 1970, leading Wagner's Parsifal.

He conducted in concerts with many leading orchestras. With the London Symphony Orchestra he made a pioneering recording of Mahler's Ninth Symphony, and conducted such leading orchestras as the Amsterdam Concertgebouw Orchestra. He was known for his calm platform demeanor and lack of flashiness. He was always praised for his competence and way with balancing orchestral sounds to make outstanding effects, though some detractors sometimes rated him as highly competent and sometimes less than inspired.