When Does "A Complete Unknown" (2024) Take Place?
"A Complete Unknown" is a historical fiction film written by James Mangold with Jay Cocks that released December 25th, 2024. So when is "A Complete Unknown" set?
It takes place in the years:
We know this because it depicts some key moments in the life of real-world musician Robert Zimmerman a.k.a. Bob Dylan, starting with his arrival in New York City in hopes of meeting folk musician Woody Guthrie. This occurred in the real world in January of 1961 AD.

1961 AD - 1965 AD
We know this because it depicts some key moments in the life of real-world musician Robert Zimmerman a.k.a. Bob Dylan, starting with his arrival in New York City in hopes of meeting folk musician Woody Guthrie. This occurred in the real world in January of 1961 AD.
Furthermore, the movie very early on includes a time-setting white-on-black title card that reads "1961".
Soon, the characters are shown watching and reacting to the television news broadcasts covering the famous Turkish/Cuban Missile Crisis, which lasted from October 16th, 1962 AD to October 28th, 1962 AD in the real world. So it is certainly October of 1962 AD at this point.
Midway through the narrative Dylan and fellow real-world singer-songwriter Joan Baez are seen singing on a stage below a banner proudly displaying "MONTEREY FOLK FESTIVAL 1963". The first Monterey Folk Festival was held from May 17th, 1963 AD to May 19th, 1963 AD in the real world. Therefore, it's most likely reached May of 1963 AD.
A few later shots follow suit and include a "1964 NEWORT FOLK FESTIVAL 1964" banner. So we know the audience passes through 1964 AD, as well.
The story finds its climax at the 1965 Newport Folk Festival, specifically an infamous performance that happened on July 25th, 1965 AD in the real world while the characters perform on a stage above that year's "NEWPORT FOLK FESTIVAL 1965" banner. So presumably, it’s certainly July of 1965 AD at the end of the film.