The son of a lawyer, Teller was born in the Hungarian capital Budapest. Having attended the Institute of Technology there, he continued his education in Germany at the universities of Karlsruhe, Munich, Leipzig (where he obtained his PhD in 1930), and Göttingen. He left Germany when Hitler came to power in 1933. After a short period in Denmark and London, he emigrated to America where in 1935 he took up an appointment as professor of physics at George Washington University. During the war he worked in the theoretical physics division at Los Alamos on the development of the atom bomb, resuming his academic career in 1946 at the University of Chicago. Teller moved in 1953 to the University of California at Berkeley, where he remained until his retirement in 1975.

Teller is often referred to as the ‘father of the hydrogen bomb’. Insofar as he made the initial proposal in 1942, worked longest on the project, and campaigned most vigorously for its completion, the description is accurate. If, however, the phrase is taken to mean that the bomb exploded in 1951 was Teller's own design, the description is misleading.

From the mid-1940s Teller was working with three possible bomb designs, A, B, and C. By 1947 it was clear that B would fail and that C, though viable, would produce too small an explosion to be worthwhile. Research effort was therefore concentrated on design A which required horrendous amounts of calculation; these were carried out by the mathematician Stanislaw Ulam. In 1950 President Truman, following the Russian atomic bomb explosion, ordered the program to be speeded up. At this point Ulam revealed that option A was hopeless, requiring such massive amounts of tritium to be virtually unworkable. At this point Teller found himself, after nearly a decade of intensive and costly research, without any viable design or idea in response to the President's urgent call.

By early 1951 Ulam and Teller had worked out a fourth and effective method, the origin of which remains a matter of dispute. The basic problem of the early designs was that the bomb would fly apart under the explosion of the fission device before the fusion material was sufficiently compressed. Ulam's solution was to use x-rays from the fission device to produce compression waves long before any shock waves could strangle the planned thermonuclear reaction. While Hans Bethe attributes the idea to Ulam, Teller has claimed the credit for himself, insisting that “Ulam triggered nothing.”

After the successful explosion of the first thermonuclear device in 1951 Teller moved to the Livermore laboratories, which were performing research for the Atomic Energy Commission. Shortly afterward, loyalty hearings were held against Oppenheimer. Teller, despite much pressure from the scientific community, decided to testify against him and although he did not accuse Oppenheimer of disloyalty, still less of treason, he did complain that “his actions frankly appeared to me confused and complicated…I would personally feel more secure if public matters could rest in other hands.” In the charged atmosphere of the 1950s this contributed to the withdrawal of Oppenheimer's security status and to the ostracism of Teller by many of his old friends and colleagues. For ten years Teller was neither invited to nor visited Los Alamos.

Teller continued to be a powerful figure in American science after his retirement from Berkeley in 1975. In 1984, for example, he advised Washington that the influential paper of Carl Sagan and his colleagues on the dangers of a nuclear winter was far from convincing. At Livermore he worked on and campaigned vigorously for the Strategic Defense Initiative (SDI), better known as ‘Star Wars’. The key ingredient of SDI was the x-ray laser, which would supposedly destroy enemy missiles in space. Teller had to face charges against the program from Hans Bethe that it was “unwieldy, costly, easily countered, destabilizing, and uncertain.” Despite these and other charges, and despite a tendency for supporters of the SDI to promise more than they could ever hope to deliver, Teller's support for the project never wavered. He published a forthright defense of the program in his book Better a Shield than a Sword (1987). However, in 1993 the project was abandoned amid accusations that test results had been distorted. The SDI department was renamed the Ballistic Missile Defense Organization and it now researches ways of eliminating enemy missiles nearer the ground.