There were three Moscow Trials that included the Case of the Trotskyite-Zinovievite Terrorist Center (Zinoviev-Kamenev Trial, aka "Trial of the Sixteen," 1936), the Case of the Anti-Soviet Trotskyist Center (Pyatakov-Radek Trial, 1937), and the Case of the Anti-Soviet "Bloc of Rights and Trotskyites" (Bukharin-Rykov Trial, aka "Trial of the Twenty-One," 1938).
The defendants of these were Old Bolshevik party leaders and top officials of the Soviet secret police. Most defendants were charged under Article 58 of the RSFSR Penal Code with conspiring with the western powers to assassinate Stalin and other Soviet leaders, dismember the Soviet Union, and restore capitalism.
The Moscow Trials led to the execution of many of the defendants. They are generally seen as part of Stalin's Great Purge, an attempt to rid the party of current or prior oppositionists, especially but not exclusively Trotskyists, and any leading Bolshevik cadre from the time of the Russian Revolution or earlier, who might even potentially become a figurehead for the growing discontent in the Soviet populace resulting from Stalin's mismanagement of the economy. Stalin's hasty industrialisation during the period of the First Five Year Plan and the brutality of the forced collectivisation of agriculture had led to an acute economic and political crisis in 1928-33, a part of the global problem known as the Great Depression, and to enormous suffering on the part of the Soviet workers and peasants. Stalin was acutely conscious of this fact and took steps to prevent it taking the form of an opposition inside the Communist Party of the Soviet Union to his increasingly autocratic rule.
Stalin, Grigory Zinoviev, and Lev Kamenev formed a ruling triumvirate (so called troika, distinguish it from NKVD troika) in early 1923 after Vladimir Lenin had become incapacitated from a stroke. In the context of the series of defeats of communist revolutions abroad (crucially the German revolutions of 1919 and 1923 but also later the Chinese Revolution of 1927) which left the Russian Revolution increasingly isolated in a backward country, enabled the troika to effect the marginalization of Leon Trotsky in an internal party political conflict over the issue of Stalin's theory of Socialism in One Country. It was Trotsky who most clearly represented the wing of the CPSU leadership which claimed that the survival of the revolution depended on the spread of communism to the advanced European economies especially Germany. This was expressed in his theory of Permanent Revolution.
A few years later, Zinoviev and Kamenev joined the United Front in an alliance with Trotsky which favored Trotskyism and opposed Stalin specifically. Consequently, Stalin allied with Nikolai Bukharin and defeated Trotsky in a power struggle. Trotsky was expelled from the Soviet Union in 1929 and Kamenev and Zinoviev temporarily lost their membership in the Communist Party. Zinoviev and Kamenev, in 1932, were found to be complicit in the Ryutin Affair and again were temporarily expelled from the Communist Party. In December 1934, Sergei Kirov was assassinated and, subsequently 15 defendants were found guilty of direct, or indirect, involvement in the crime and were executed. Zinoviev and Kamenev were found to be morally complicit in Kirov's murder and were sentenced to prison terms of ten and five years, respectively.