How did Soviet leaders Khruschev and Gorbachev try to undo the worst abuses of the Stalin era, and to what extent were their reforms successful?

Nikita Khrushchev's contributions to the end of Stalinism have often been, fairly, one might add, overshadowed by his contributions to the heightening of the Cold War tensions between the Soviet Union and its satellites on the one side and the United States and its allies on the other. Khrushchev did, however, play a major role in delegitimizing the "cult of personality" Joseph Stalin had created during the unbelievably brutal years of the latter's rule. 

That Khrushchev was serious about moving the Soviet Union away from the indescribably repressive atmosphere in which his predecessor and former ally Stalin had functioned was evident in the text of his most famous speech, which occurred during the Communist Party of the Soviet Union's 20th Congress. On February 25, 1956, Khrushchev, having successfully outmaneuvered his rivals for power following Stalin's death, gave an impassioned speech before the Party leadership in which he condemned Stalin's "cult of personality" and, more significantly, his predecessor's perversion of socialist revolution for the purposes of self-preservation. As Khrushchev stated in this speech, Stalin had utilized the Party apparatus for the nefarious purpose of eliminating his enemies. In the following passage, the newly-established leader stated:

"Stalin originated the concept 'enemy of the people.' This term automatically made it unnecessary that the ideological errors of a man or men engaged in a controversy be proven. It made possible the use of the cruelest repression, violating all norms of revolutionary legality, against anyone who in any way disagreed with Stalin, against those who were only suspected of hostile intent, against those who had bad reputations."

By delegitimizing the cult of personality of Stalin, Khrushchev made it politically-palatable for Soviet Party members to strike a more moderate tone and to pursue economic policies less-inhumane and less-counterproductive than those forced through by Stalin.

Mikhail Gorbachev played an instrumental role in eliminating, at least for a time, the totalitarian political system that had dominated Russia and its surrounding territories (i.e., colonies) for many years. His policies of perestroika and glasnost--restructuring of the economy and opening of the political atmosphere to freedom of expression--were without precedent in Russian history. People previously imprisoned under the harshest conditions for speaking their minds were now free to criticize their leaders and advocate alternative political and economic policies. Fortunately for the vast Russian Empire but unfortunately for the vanity of the Russian populace, his policies enabled the reemergence of independent nations along Russia's periphery--a major bone of contention for Russian nationalists today who remain nostalgic for the lost empire that had its seat in Moscow. Also unfortunate for the Russian people, the end of the monopoly on power previously enjoyed by the Communist Party left a vacuum into which moved not just legitimate democratic movements, but avaricious oligarchs, gangsters, and former members of the secret police (one of whom rules with iron fist today: Vladimir Putin) all of whom put their own interests ahead of the populations.