Short answers, pulled from the story.
The People's Commissariat for Internal Affairs operated as the secret police of the Soviet Union from 1934 to 1946. It emerged from earlier agencies like the Cheka and OGPU before transforming into an all-USSR security force in 1934.
At least 1.3 million people were arrested and 681,692 executed for crimes against the state between 1937 and 1938. The Gulag population swelled by 685,201 under Yezhov while at least 140,000 prisoners died of malnutrition, exhaustion, and exposure.
Genrikh Yagoda led the agency from 1934 until 1936 before Nikolai Yezhov took over until 1938. Lavrentiy Beria directed operations from 1938 to 1945 and Sergei Kruglov held the position briefly in 1946.
The NKVD executed tens of thousands of Polish political prisoners during 1940 and 1941 including at the Katyń massacre where Vasily Blokhin personally oversaw executions. On the 26th of November 2010, the State Duma acknowledged Stalin's responsibility for executing 22,000 Polish POWs.
Many scientists and engineers arrested for political crimes were placed in special prisons known as sharashkas where they continued their work under comfortable conditions. Some inmates became world leaders in science and technology after release including Sergey Korolev who designed the first human space flight mission in 1961.