(Based on:) http://www.historyaccess.com/juliusandethelro.html

In 1951, the Rosenbergs were found guilty in a federal courtroom of conspiring to commit espionage. Judge Irving R. Kaufman sentenced them to die, saying they had stolen America’s most precious military secret, the atomic bomb, and given it to the Soviet Union. The Rosenbergs maintained their innocence. Many people in America believed that the couple had been framed by a government caught up in the Red Scare of 1949-54. Both eventually became "the most internationally celebrated martyrs since Captain Dreyfus." (Ted Morgan)

Julius Rosenberg, born 1918, the son of Polish immigrants, grew up poor on Manhattan’s Lower East Side, a studious boy interested in rabbinical studies. His left wing ardor grew in 1934 when he enrolled at City College of New York, then a hotbed of American radicalism, in the depths of the Great Depression. Young Trotskyists and Stalinists sometimes engaged in passionate debates about humanity's future in lunchroom alcoves. Many students felt that Marxism offered solutions to humanity; Julius became active in the Young Communist League.

He met Ethel Greenglass on New Year’s Eve, 1935, at a union fundraiser in New York City. Born on September 25, 1915, she, too, was a product of the Lower East Side tenements, a bright young woman (she graduated from high school at age 15) who had been stagestruck as a girl and aspired to become a performer. In the middle 1930s, she lost her job as a clerk for a shipping company, apparently because of her activism.

Ethel and Julius married in the spring of 1939 after Julius graduated from CCNY with a degree in electrical engineering. He got a job in Brooklyn with the U.S. Army Signal Corps. They had two children, Michael (born in 1943) and Robert (1947).

According to many scholars and observers, a convincing version of events is offered by historians Ronald Radosh and Joyce Milton in their 1983 book "The Rosenberg File." In 1943, Aleksandr Feklisov, a KGB officer at the Russian Consulate in New York, was given the name of Julius Rosenberg as a potential recruit for his group of secret agents. Feklisov met Rosenberg, who agreed to spy for the Soviets and said he would seek out others who would also engage in espionage. Julius stole technical secrets and handed them over to Feklisov, including a proximity fuse, used in anti-aircraft weaponry.

Meanwhile, Ethel’s brother, David Greenglass, had gotten a job as a machinist in the Manhattan Project, America’s massive effort to build an atomic bomb. Julius recruited David into the spy network, obtained from him data about the inner workings of the bomb, and passed this to the Soviets. After the war Julius continued spying for the Soviet Union, turning over military and industrial information. Ethel knew of his work but her participation in it was minimal. 

Federal agents discovered the Rosenbergs via a circuitous route. Another spy for the Soviets, a top scientist named Klaus Fuchs, was arrested in Great Britain in January, 1950, and quickly signed a confession ,leading  investigators to Harry Gold, a longtime Soviet spy in the United States who had collaborated with David Greenglass. Gold named Greenglass to the FBI; Greenglass fingered the Rosenbergs and agreed to testify against them.

At Sing Sing Prison in New York, on June 19, 1953, at 8 p.m., Julius Rosenberg died on the electric chair. A few minutes later, Ethel his wife died in the same conditions.It is said that a few Rosenberg supporters were astounded that the government would execute two innocent peole. Meanwhile, many Americans were relieved to hear of the deaths.

But did Julius Rosenberg steal the "atomic secret"? Julius and Ethel Rosenberg were guilty of "putting into the hands of the Russians the A-bomb years before our best scientists predicted Russia would perfect the bomb", which led to "the Communist aggression in Korea, with the resultant casualties exceeding 50,000." This was not accurate. Several spies did much more damage to Western interests than the Rosenbergs. For example, material stolen by Klaus Fuchs was far more important. There's no question that Julius Rosenberg committed a serious crime, but they were sentenced to die in the hope that they would identify collaborators in exchange for life imprisonment. David Greenglass said in 2001 that he lied on the witness stand about her involvement. 

Note that the French historian Alain Decaux wrote a play about the couple (Les Rosenbergs ne veulent pas mourir)