
On the 24th of February, 1956, the private session of the 20th Party Congress (that is, the meeting during which the USSR appointed the leadership for every SSR in the U) began; at this point, only Higher-ups from inside the party were allowed, no journalists, no allies, no delegations of any sort. At this meeting, Nikita Khrushchev gave probably the most famous speech of his life, "On the Cult of Personality and Its Consequences". Inside the USSR, this was sometimes called "The Secret Speech". In attendance, for reasons that will become clear, were one hundred former Party members that had been released from gulags.
The speech was exfiltrated by the

Mossad

and, although widely disseminated, it was not until much later (in 1989, under Gorbachev's glasnost policies) that the official text was published in the USSR. There is suspicion that Khrushchev himself encouraged the leaks, but in any case the text of the speech was reproduced to be read throughout the USSR.
The contents of the speech, which was four hours long, detailed the cult of personality around Stalin, his brutal repression of the opposition, the liquidation of the kulaks, all of that. It was a fairly unambiguous denouncement of Stalin, though it does have plenty of positive things to say about some of his policies. (It was still the USSR; "authoritarianism" wasn't exactly as dirty a word as it is around these parts.) There was, throughout the speech, constant criticism of the cult of personality and an endorsement of collective leadership, which made it unpopular with communist states that still relied on the cult of personality. (

Mao criticized the speech and denounced Khrushchev as revisionist. As much as Mao hated Stalin, this was a blow to his legitimacy.)
The reaction was fairly mixed, to say the least. It completely wrecked the Communist Party USA (which lost, according to the NYT, 30k members almost immediately and was a fringe movement just a year later:
https://www.nytimes.com/2017/04/29/opinion/sunday/when-communism-inspired-americans.html ). The "Stalin did nothing wrong" contingent ran out of steam when even the Premier of the USSR wanted no part of it. Within the USSR and the rest of the Eastern Bloc, a large number of people didn't know what to think. Of course, they had to take Stalin's name out of the national anthem which was performed without lyrics for the next twenty years until revised lyrics were composed under Brezhnev. By 1961, Stalingrad was no more and Volgograd took its place.
Here's what Wikkypeeja has to say:
https://en.wikipedia.org/wiki/On_the_Cult_of_Personality_and_Its_Consequences .
Text of the speech, in the form of a PDF from archive.org, is attached below:
on_the_cult_of_personality_and_…