This was Andrey Tarkovsky's first film directed outside of the USSR. It was supposed to be filmed in Italy with the support of Mosfilm, with most of the dialogue in Italian. When Mosfilm support was inexplicably withdrawn, Tarkovsky used part of the budget provided by Italian State Television and French film company Gaumont to complete the film in Italy and cut some Russian scenes from the screenplay, while recreating Russian locations for other scenes in Italy.
At one point, Domenico questions mathematics, displaying that "1+1 not equals 2" with two drops of olive oil. This is a reference to one of Guerra's collaborations with Michelangelo Antonioni, Red Desert.
The trivia item below may give away important plot points.
The final shot, where Gorchakov's house - complete with hills and a pond - is translated into the central aisle of the abbazia of San Galgano, was achieved using forced perspective and miniature models of the Russian landscape.