Since the 90's, the studio has produced a large number of comic book movies based off licensed Marvel properties.
Due to the fact that Fox's licensed Marvel films predate the creation of Marvel Studios' Marvel Cinematic Universe, there exist a number of legal issues regarding certain characters. It has been confirmed that both Fox and Marvel Studios share rights to Quicksilver and the Scarlet Witch, allowing for alternate depictions of the characters to appear in both X-Men: Days of Future Past and Avengers: Age of Ultron. However, the Avengers films are unable to mention key elements of the characters' histories, namely their father Magneto, their affiliation with the Brotherhood of Mutants, and their genetic status as mutants. Likewise, Fox is barred from mentioning the Avengers or the Vision and Crystal, Scarlet Witch and Quicksilver's respective love interests.
In addition, thanks to Fox's ownership of the X-Men franchise, Marvel is barred from even using the word "mutant" in its various productions, which lead to the general term "Gifted" being used to describe superhumans in the series Agents of S.H.I.E.L.D. and other MCU productions. Longtime X-Men writer Chris Claremont has stated that he believes Marvel's sudden interest in the Inhumans was born out of a desire to use mutant-like characters in their films and TV shows without running into more legal red tape from Fox.
Additionally, the Skrulls fall into a similar area, with Fox being able to claim partial ownership due to their ownership of the Fantastic Four franchise. It would also appear that Fox has complete ownership of the Badoon, which prevented the aliens from being used in the Guardians of the Galaxy film.
Fox also held rights to the Daredevil franchise for a number of years, but ultimately lost them due to their failure to enter into production on a new Daredevil reboot before the required deadline. The rights have since returned to Marvel, and the character will be introduced into the Marvel Cinematic Universe via a live-action TV series.
X-2: X-Men United (2003)
X-Men: The Last Stand (2006)
X-Men Origins: Wolverine (2009)
X-Men: First Class (2011)
The Wolverine (2013)
X-Men: Days of Future Past (2014)
Fantastic Four franchise
Fantastic Four (2005)
Fantastic Four: Rise of the Silver Surfer (2007)
The Fantastic Four (2015)
Nick Fury: Agent of S.H.I.E.L.D.(1998)