This movie is remarkable, all the moreso because of the the amount of inadvertent prophecy that takes place during the course of it. Shoes of the Fisherman is a phrase that is sometimes used to refer to the office of the Pope, the Bishop of Rome; the See of Peter, the Chair of Peter, etc., various other historical and scriptural references are a kind of ecclesial shorthand.
This story takes place during the height of the Cold War, when it was not primarily a two-way confrontation, but rather seemed to threaten to become a three-way contest with the seeming emergence of China as a communist power independent from the Soviet Union.
Archbishop Kyril (Anthony Quinn), longtime political prisoner of the Soviets, is released (the exact reasoning for this we are never told) by his long-time captor (the Soviet premier, played by Laurence Olivier). He is released to Rome, where he is installed as a cardinal for his faithfulness to the church. Shortly thereafter, the pope (John Gielgud, who is on screen for only a few minutes) dies, and an election takes place. Remarkably, Kyril the Russian is elected pope, after giving a moving account of his time in captivity to assembled cardinals weary of the election process, and shortly thereafter commits the church to a risky mercy mission to prevent war from breaking out between the communist powers.
Subplots include a very timid (by today's standards) love triangle by a reporter, his wife and his soon-to-be ex-mistress, and an ecclesiastical tribunal examining the works of a radical theologian.
This movie had unprecedented vantage of the Vatican for showing the process of a pope's death and succession. The small historical niceties are shown and explained throughout the film. One gets a sense of the procedure and the history.
What makes this movie so remarkable is that it was released a full decade before the election of another pope from the communist block. In 1968 it was considered very shocking to consider a non-Italian pope, much less one coming from behind the Iron Curtain.
Another prophetic instance is in the ecclesiastical trial of the radical theologian -- during his defense, this theologian even uses the words 'cosmic Christ', and recounts a theological formulation very similar to that which later found expression through Matthew Fox (who used the phrase 'cosmic Christ' in one of his book titles), who was silenced by his Roman order, and who finally had to leave the church to remain true to his convictions.
Just how the scriptwriters and director could have foreseen these so far in advance is a mystery.
The film is beautiful, well-acted, a bit long in parts, moving in others (the scene where Kyril, during an 'escape' from the Vatican comes across a dying Jewish man and begins to recite Jewish prayers is one of the more moving scenes theologically of any film), and gives a glimpse into a usually hidden, and largely unchanging world.