The British Invasion
This was a moniker applied by the American media to the huge influx of British pop music, notably Rock and Roll, to American consumers in the 1960s. While it's traditionally considered to have started when British bands started headlining concerts in America, starting with The Beatles on The Ed Sullivan Show on February 9th, 1964, it actually started the year before. Beatlemania -- not just the music, but the entire phenomenon -- attracted the attention of news agencies and talk show hosts in November 1963. Capitol Records finally realized then that the Beatles were in fact marketable, marketed the band like crazy, and their first American hit single hit the charts around Christmas 1963.
The key here is this actually was a cycle, as most of these bands were actually influenced by American rock and blues, including some featured in the Jayne Mansfield film The Girl Can't Help It. Many of these bands took it to the next level, and not just the oft-cited Beatles; consider bands who laid the groundwork for hard rock and heavy metal, such as The Rolling Stones, The Kinks, and The Who. (It may not be a coincidence that the offshore pirate radio boom took place around the same time, giving bands much-needed airplay that The BBC didn't have time for until the launch of Radio 1 in 1967.)
The first invasion may have just been in the 1960s, but it turned full circle when American artists took the sound yet further, such as Jimi Hendrix and early heavy metal bands. This lead to the Second British Invasion in the late 1970s and early 1980s, with Punk Rock, the New Wave of British Heavy Metal (or NWOBHM), and New Wave (not to be confused with the heavy metal). This second wave of British music was brought on, perhaps inadvertently, by MTV. In their early years, MTV was desperate for any music videos they could get their hands on, and it just so happened that most of the music videos of that time were coming out of Britain, thanks to shows like Top of the Pops that helped to popularize the format over there in The Seventies. By contrast, most American music videos during the same period were merely videotaped concert performances. MTV threw these British videos on the air, and the bands suddenly saw themselves developing screaming American fanbases virtually overnight. Combine this with the creative slump in American popular music following the anti-disco backlash of the late '70s/early '80s, and British pop and rock took over the American music market.
One odd influence here is that, anytime there is a large influx of artists of any media from "across the pond" (such as Oasis or Radiohead), it is often labeled as a British Invasion by enthusiasts of that particular medium. For instance, when British Comic Book talents like Alan Moore and Grant Morrison started coming over in 1980s America to make their mark, their tremendous success was likened to being a comic book British Invasion.