Nearly 20 years after the fall of the Soviet Union, people from Slavic countries have become a reliable presence in Hollywood. Suddenly we’re a long way from Boris and Natasha’s “Must get Moose and Squirrel.”

Filmmakers have turned to Eastern European settings and themes in movies like “We Own the Night,” about the Russian Mafia in New York, David Cronenberg’s  “Eastern Promises,” set in Eastern Europe, and the late Anthony Minghella’s mixing of the Brits and the Serbs in “Breaking and Entering.”

But most striking is the way Eastern European actors and directors have been flourishing lately in Hollywood. There’s Ukraine’s Olga Kurylenko, who stars as the latest Bond Girl opposite Daniel Craig in “Quantum of Solace.” Besides Kurylenko, Kiev-born Mila Kunis found success...