Short answers, pulled from the story.
Zamyatin is best known for his 1921 dystopian science fiction novel We, set in a futuristic police state called the One State. It became the first work banned by the Soviet censorship board and directly inspired later dystopian novels including Aldous Huxley's Brave New World, George Orwell's Nineteen Eighty-Four, and Ayn Rand's Anthem.
Zamyatin used literature to satirize and criticize the Soviet Union's enforced conformity and totalitarianism despite being an Old Bolshevik himself. He arranged for his banned novel We to be smuggled to Western publishers, resigned from the Union of Soviet Writers in 1929 rather than recant his views, and eventually requested personal permission from Joseph Stalin to leave the country.
Zamyatin died of a heart attack on the 10th of March 1937 in Paris. He was buried at the Cimetière de Thiais in the Parisian suburb of the same name. His death was unreported in the Soviet press.
We is set in the far future in the One State, a glass-walled city where citizens are identified only by numbers, life is governed by Taylorist formulas, and a secret police called the Bureau of Guardians enforces total surveillance. The protagonist D-503, chief engineer of a spaceship called the Integral, is drawn into a rebel organization named MEPHI that aims to destroy the Green Wall surrounding the city and reunite its people with the outside world.
In 1931, Zamyatin wrote directly to Soviet General Secretary Joseph Stalin requesting permission to leave with his wife, describing his situation as "the death sentence that has been pronounced upon me as a writer here at home." He also asked Maxim Gorky to intercede on his behalf. Gorky did so, and Zamyatin left the Soviet Union in November 1931.
Zamyatin's novel We directly inspired Aldous Huxley's Brave New World (1932), Ayn Rand's Anthem (1938), George Orwell's Nineteen Eighty-Four (1949), Kurt Vonnegut's Player Piano (1952), and Ursula K. Le Guin's The Dispossessed (1974). Vonnegut acknowledged that he ripped off the plot of Brave New World, which he said had itself been ripped from We. We received a Prometheus Award in the Libertarian Futurist Society's Hall of Fame category in 1994.