Born in Rostov-on-Don (modern-day Rostov Oblast of Russia) as Rostislav Ivanovich Plyat, the future actor was so obsessed with theatre that he decided to "correct" his name at the passport office to make it more euphonious and memorable.

[5] During the Great Patriotic War Plyatt stayed in the sieged Moscow, gave theatre performances and worked as a radio host, regularly crossing the city during heavy bombings.

They appeared in two leading roles in the popular The Rest Is Silence play, the Mossovet stage adaptation of Make Way for Tomorrow where Ranevskaya performed till the end of her career; Plyatt's Barkley Cooper is universally praised as the peak of his acting skills.

[3][5][6] Among Plyatt's famous movie roles were Bubentsov in Grigori Aleksandrov's Springtime (1947), Petukhov in A Groom from the Other World (1958) and landlord in Strictly Business (1962), both by Leonid Gaidai, Dankevich in Sergey Mikaelyan's Going Inside a Storm (1965) and pastor Schlag in Tatyana Lioznova's Seventeen Moments of Spring mini-series (1973).

He also worked a lot as a voice actor, narrating films and cartoons, dubbing foreign movies and performing in radio plays.