As of now, there is no official release date announced for "Poor Things." However, IMDb does have the release date listed as 2022, which narrows it down a bit.
To speculate where the release date could land in the coming year, we can look to Lathimos's most recent film, "The Favourite." By March 2017, "The Favourite" was rounding out its cast, with Joe Alwyn joining Nicholas Hoult, Stone, Colman, and Weisz (via The Hollywood Reporter). Production wrapped a few months later, as IndieWire reported. Finally, the film premiered at the Venice Film Festival in September 2018, then received a wider theater release in November of 2018.
"Poor Things" is currently in the stage of rounding out its casting, with several names now attached to the project. Searchlight Pictures and Film4 will likely have awards season aspirations for the movie, too, considering this is Yorgos Lanthimos' feature-length follow-up to "The Favorite." Thus, going off of this information and the previous movie's timeline, we could see "Poor Things" released in late 2022 following a premiere at one or more fall film festivals.
