Short answers, pulled from the story.
The Venona project was a United States counterintelligence program run by the Army's Signal Intelligence Service and later the NSA, operating from the 1st of February 1943 until the 1st of October 1980. Its purpose was to decrypt and translate encrypted messages sent by Soviet intelligence agencies including the NKVD, KGB, and GRU. Over its 37-year duration, analysts decrypted and translated approximately 3,000 messages.
The Soviets made a critical error by producing roughly 35,000 pages of duplicate one-time pad key numbers under pressure from the German advance on Moscow during World War II. Reuse of a one-time pad undermines its security, and American cryptanalysts at Arlington Hall detected the duplication. Lieutenant Richard Hallock first noticed the reuse in Soviet Trade traffic, and Meredith Gardner made the first decisive break into the code on the 20th of December 1946.
Venona revealed that multiple Soviet agents had penetrated the Manhattan Project at Los Alamos. Klaus Fuchs, identified under the code names CHARLES and REST, provided the Soviets with the blueprint for the Trinity device and data on atomic bomb design. David Greenglass, code name KALIBER, also passed information, and Venona decrypts additionally identified two unresolved sources: "Quantum," identified in KGB archive notes as Boris Podolsky, and "Pers," identified as engineer Russell W. McNutt from the Oak Ridge uranium processing plant.
Venona identified Julius Rosenberg under the code name LIBERAL and established that he was guilty of espionage, passing information on the proximity fuze, the Lockheed P-80 jet fighter, and thousands of classified reports from Emerson Radio. Harry Gold's confessions, which followed his identification through Venona, led investigators to David Greenglass, who then testified against Julius and Ethel Rosenberg. Venona showed Ethel served as an accessory and participated in recruiting her brother for atomic espionage.
Army Chief of Staff Omar Bradley decided to deny President Truman direct knowledge of the Venona project, citing concerns about the White House's history of leaking sensitive information. Truman received counterintelligence findings derived from Venona but was never told the material came from decoded Soviet ciphers. This secrecy backfired: Truman distrusted FBI director J. Edgar Hoover and suspected the intelligence reports were politically exaggerated.
Philby learned about Venona in 1949 as British SIS liaison to American intelligence. The FBI told him that an agent code-named "Homer" had been identified from a 1945 message traced to the British Embassy in Washington. Without knowing Maclean's code name, Philby deduced Maclean was Homer and advised Moscow to extract him. This led to Maclean and Guy Burgess fleeing to Moscow in May 1951.