There are a lot of funny jokes dedicated to Russian people and life in Russia. But only a small number of them can be joined into the whole trend with its own rules and history. "In Soviet Russia" or "The Russian Reversal" is just that unique trend. It was created for describing another, "Red" Russia, but was given a new birth our days.  

“In Soviet Russia” or “the Russian Reversal” is a very easy way to made a good absurd joke. It was created by stand-up comedian Yakov Smirnoff. The joke was extremely popular in the late 80’s, but only in America. Then it fell out of vogue in the 90’s, and has been given new life among various online communities. The important part is that now this joke has become widespread among Russian Internet users, who now create jokes about themselves and their country. 

Origin
Ukrainian-born American comedian Yakov Smirnoff was popular in the 1980’s for his act that used wordplay to satirize the differences between his new life in the US and his old life in what was then part of the Soviet Union.
One style of joke in particular was known as the Russian Reversal, or simply referred to as, “In Soviet Russia…”
Here is a Miller Lite beer advertisement with the participation of Yakov Smirnov, who uses his crowning joke.
 
The phrase «In Los Angeles, you can always find a party. In Soviet Russia, the Party can always find YOU!» can't be so easy translated into Russian, as there is a play on words, where the word “party” can mean either “a social gathering” of “a political group”.
For example, another joke based on that words play: «The first time when I went to a restaurant, the waiter asked me: „How many people are in your party?“, and I answered: „More than 600 000 000 people“»
All of Smirnoff's original "In Soviet Russia" jokes made use of formulaic wordplay that carried Orwellian undertones. For example, two common jokes of this type run "In America, you listen to man on radio. In Soviet Russia, man on radio listen to you!" and "In America, you watch television. In Soviet Russia, television watch you!" The joke alludes to video screens that both reproduce images and monitor the citizenry, as in the novel 1984.

Smirnoff's use of English allowed him to smooth over grammar differences in transitioning from the setup to the punchline. For example, he omits the articles "a" and "the" in the first reversal joke above, to better preserve the congruence. Also, verbs are often left unconjugated.
Unfortunately, Yakov’s popularity waned through the 90’s, as did his jokes.

 
Old Joke, New Reality
The Russian Reversal was given a new birth in 2001, in season 6 episode 9 of Fox’s King of the Hill Bobby aspires to be a comedian and meets Yakov in Branson, Missouri; performing his own twist on the Russian Reversal.

In America, you put ‘In God We Trust’ on your money.
In Russia, we have no money!

The same year, Family Guys popular animated series also made a Russian Reversal reference. In Season 2, episode 16, entitled There’s Something About Paulie, Peter gets a rental car with a voice-navigate system. One of the optional voices Peter tries out is an impression of Yakov Smirnoff, delivering the following lines…

In Soviet Russia, car drives you!
Turn right at fork in road.
In Soviet Russia, road forks you!


In 2002, The Simpsons also referenced Yakov Smirnoff’s Russian Reversal in the 13th episode of the 13th season, entitled “The old man and the key.” In the episode, Abe Simpson and his girlfriend Zelda visit Branson, Missouri where they see a Yakov Smirnoff comedy review.
“In Soviet Russia review watches you”.
Although the exact cause is unknown, the popularity of “In Soviet Russia” seemed to peak in 2005 and today the joke successfully lives without its creator. A popular hypothesis about the 2005 popularity peak is that reruns of Family Guy, The Simpsons and King of the Hill were the cause. However, many of those people, who now make new “Russian Reversal” jokes, never watched any of these episodes.
  Internet culture often links the phrase “In Soviet Russia” with many absurd and topsy-turn pictures, videos and stories. At most, it has nothing to do with real life in Russia. Morevoer, the illustrations for that joke can be made anywhere else but in Russia. Still this joke surely describes how foreigners see that country – a strange and amazing Wonderland, where any madness is possible. And of course, it's a good way for Russians to laugh at themselves.

Examples from Cinema and Music:
Why does a dog wag its tail? Because a dog is smarter than its tail. If the tail were smarter, the tail would wag the dog.
The Movie “Watch the Dog”
Who washes the towel? The towel washes me!
A New Girl, 11th episode
— This year I'm getting paid. Hammond's check cleared, or I wouldn't go on this wild-goose chase.
— You're going to the only place where the geese chase you.
Movie «The Lost World. Jurassic park II» 
— My father can't play piano.
— No need to. This piano plays me!
Movie «Coraline»
Sometimes you eat the bear ... and sometimes the bear eats you.
Movie «The Big Lebowski»
Things you own end up owning you.
Movie "Fight Club"
The things you own, own you
Papa Roach — Between Angels and Insects
I don't like the drugs, but the drugs like me
Marilyn Manson — I Don't Like the Drugs
Don't waste your time or time will waste you
Muse — Knights Of Cydonia

Other Examples:
In America, you throw a birthday party. In Soviet Russia, birthday party throws you! 
In America, you watch television. In Soviet Russia, television watches you! 
In America, you break laws. In Soviet Russia, laws break you! 
In America, you open gifts. In Soviet Russia, gifts open you! 
In America, you listen to radios. In Soviet Russia, radios listen to you! 
In America, your job determines your marks. In Soviet Russia, Marx determines your job! 
In America, you assassinate presidents. In Soviet Russia, presidents assassinate you! 
 In America, you watch Big Brother. In Soviet Russia, Big Brother watches you!

Sources: knowyourmeme.com Wikipedia Lurkmore Youtube Demotivators.ru
Julia Alieva