Taken from a previous answer:

Elton John indeed played a show in Moscow in 1979, the recording of which isn't exactly new but which was captured in the feature length film To Russia With Elton. He was not the first Western pop act to play in Russia; Cliff Richard played in Leningrad in 1976, and Boney M played in Moscow in 1978 - but unlike the relatively anodyne Cliff Richard or Boney M - entertainers perhaps more in line with official Russian entertainment styles - Elton John was more firmly of the Western rock aesthetic; in Russia he performed the song 'I Think I'm Gonna Kill Myself', along with a song eulogising a Western celebrity like Marilyn Monroe ('Candle In The Wind'), a song steeped in Western leisure culture ('Pinball Wizard'), a song about a rock'n'roll act ('Bennie And The Jets'), and of course, playing 'Rocket Man' in Russia, a decade after the height of the space race.

While there are certainly examples of the powers that be in Russia attempting to shield citizens in their zone of influence from decadent Western values, they were ultimately not entirely successful; while Western pop music was unlikely to be seen on state-run television, it enjoyed a prominent role in underground counterculture, sometimes precisely because of the attempts by the state to repress it.

The book Everything Was Forever, Until It Was No More by Alexei Yurchak documents the 'the last Soviet generation'; within it, he argues that Soviet mass production of reel-to-reel tape recorders in the 1960s caused a sea-change in the ability of Russian people to hear Western music - "the circulation of Western music in the country increased exponentially". While good music, according to Yurchak, was meant to follow the 'healthy culture of common people', as opposed to the music that provoked 'unhealthy bourgeois instincts', youth in Soviet countries nonetheless gravitated towards Western music thanks to the proliferation of tape recorders allowing people to circulate music themselves, away from official channels.

This proliferation of rock music in the Soviet sphere of influence was not approved of by the authorities - Yurchak prints a Soviet cartoon from the 1970s which portrays a young fashionable rock fangirl as lazy and immoral for preferring to be indoors listening to music rather than helping her grandfather pull out a turnip in the fields - but the scale of it meant that attempts to repress it became restricted to Western acts considered particularly dangerous or ways to oppress rebellious underground types.

Famously, Václav Havel had brought back a copy of a Velvet Underground record to Czechoslovakia with him after spending six weeks in New York in 1968, and the record - passed around the Czech underground, presumably via these reel-to-reel tape recorders - became a touchstone for the Czechoslovakian underground (Havel told The Velvet Underground's Lou Reed that he couldn't really remember the cover of the record). One group who took influence from The Velvet Underground in particular were the Czech countercultural icons The Plastic People Of The Universe, whose censorship was one of the catalysts for Charter 77. This was a document against censorship of artistic expression put together by a set of people who would eventually hold many of the reins of power when communism fell, including Havel, who became President. There's a conversation between Lou Reed and Václav Havel reprinted in the book of Lou Reed's lyrics, Between Thought And Expression: Selected Lyrics, where Havel tells Reed that:

...music, underground music, in particular one record by a band called Velvet Underground, played a rather significant role in the development in our country, and I don't think that many people in the United States have noticed this.

Havel (according to Reed) also gave him a copy of a hand-written book of Velvet Underground lyrics, translated into Czech, saying that "There were only 200 of these. They were very dangerous to have. People went to jail, and now you have one."

So by 1979, when Elton played in Russia, there would have been - and in fact, there clearly were, watching the footage linked above - fans who knew his music and were very excited to see Elton perform (though the people who got tickets to see him live were very likely good members of the Communist party rather than people of the underground counterculture like Havel). For Western audiences, oddly, these fans were seated behind the much more staid and unimpressed Russian dignitaries who were presumably complaining amongst themselves about how bourgeois Elton was. Nonetheless, their presence at the show spoke of an official desire to regulate Russian preferences in rock'n'roll; similar desires to channel the enthusiasm of Russian youth for rock'n'roll can be seen in the regularly updated official list of banned groups (an example from 1985, translated, can be seen here), which includes AC/DC (banned for 'neofascism' and 'violence') and Black Sabbath (banned for 'violence' and 'religious obscurantism').

According to Philip Norman's 1991 biography Elton, his 1979 tour came at a fortune moment. Elton, by 1978, was bored playing to the same crowds, and wanted some adventure. Asked by British rock promoter Harvey Goldsmith if he'd play in Russia, he said "sure!" thinking it was likely impossible. However, Goldsmith had other ideas, and made a request in 1978 to the Russian Ministry of Culture for Elton to tour Russia. According to Norman, there was an 'Anglo-Soviet cultural treaty', upon which Russian ballet troupes would perform in Britain, and Britain would send over opera and Shakespeare and the like. This treaty was renewed in January 1979, and the official who renewed it, one Vladimir Kokonin, attended one of Elton's concerts in Oxford. At a lunch at Lancaster House in London, Kokonin announced that "we will provide music for the masses", meaning that Elton could tour.

The Elton John concerts in Leningrad and Moscow were broadcast live on BBC Radio One along with being taped for distribution on tape in Russia. According to Norman, the Russians saw it as something of a publicity coup, as a way to show that they were hip and with it, fellow kids; diplomats at London's Russian embassy were quoted as saying it was the best thing for East-West understanding since Khrushchev visited Hollywood. Elton John and Goldsmith were happy to oblige Russian requests to avoid contentious material, but the Russians apparently had no issue with 'Rocket Man' or 'I Think I'm Gonna Kill Myself' (they objected to him finishing the concert with the Beatles' 'Back In The USSR' but he did it anyway and avoided being put down a salt mine, which he had joked about before leaving England).

According to Norman, official Russian news media's assessment of Elton was ...uncertain. Pravda argued that Elton's unhappy boyhood was a product of the decaying family values in the West, while a Russian teenage magazine said that Elton's style was marked by his 'gay originality ...while some people like this style, others find it excessively naughty'. ('gay' here referring to emotional tone rather than sexuality, which Norman finds quite amusing, noting that Elton's sexuality could have led to him being imprisoned for five years in Russia at the time).