(written from a Production point of view)
20th Century Fox or Twentieth Century Fox, officially the Twentieth Century Fox Film Corporation, is one of the biggest Hollywood film studios. It is a subsidiary of 21st Century Fox, the legal successor of the News Corporation. Formed in 1935 through the merger of Fox Film Corporation (est. 1915) with Twentieth Century Pictures (est. 1933) it was for decades one of what was once colloquially known as the "Big Five" major Hollywood motion picture studios, along with Paramount Pictures.
The company made its Newman Scoring Stage available for the recording and mixing of the music for Star Trek Into Darkness and Star Trek Beyond and was thus included in the movies' credits. While this stage, then known as the 20th Century Fox Scoring Stage, was also used for Star Trek: The Motion Picture and several seasons of Star Trek: The Next Generation, the company was not credited for this contribution.
Fox was the distributor of the first six Star Wars movies, though they only co-owned the first film with Lucasfilm Ltd., until The Walt Disney Company bought Lucasfilm on 30 October 2012, thereby becoming the new owner of the entire Star Wars franchise and cutting out 20th Century Fox all together for the residual revenues (home video formats in particular) of five of the six original films,  with the first one to follow five years later when Fox itself was acquired by Disney.
Popular franchises under the Fox umbrella include, but are not limited to, Planet of the Apes, Alien, Predator, Alien vs. Predator, Die Hard, Home Alone, Ice Age, Avatar, X-Men, Fantastic Four, and Rio.
On 14 December 2017, The Walt Disney Company announced that it is acquiring most of Fox's parent company, 21st Century Fox, including the film studio,  which was approved by both companies on 27 July 2018,  but which also cost 4,000 Fox employees their jobs.  Nonetheless, this meant that the entire Marvel Comics live-action franchise, aka the Marvel Cinematic Universe, to which the X-Men and Fantastic Four belonged, was now reunited under one roof as Disney had already acquired the Marvel Entertainment holding group in 2009 – save Spider-Man owned by Sony Studios who refused to sell to Disney. Disney is now the owner of the two most successful science fiction media franchises in history, with the popular Alien/Predator and Avatar ones from Fox to boot.
To truly gauge the full extent of the combined size of the now Disney-owned franchises, one only needs to take a look at the only five films to achieve the US$2 billion plus mark as the highest grossing films of all time; of the five that did so as of August 2019, four of them are presently fully owned by Disney – the sole exception concerned Paramount's Titanic (the first to break the two billion barrier) coming in at third place and who incidentally, was forced to seek out 20th Century Fox as equal production partner when production costs were at the time spiraling out of control, and thus effectively co-owned by Disney as well. Of the approximately thirty-five films that follow in the US$1 - 2 billion range, over half are now Disney-owned.  Of these, only two originally Fox-produced/distributed films occupy places in the entire list, but it includes the studio's biggest success in its entire history, the blockbuster Avatar (2009), the all-time highest worldwide grossing film for two decades, until it was surpassed as such in July 2019 by the Marvel/Disney film Avengers: Endgame. The massive success of the now under one roof concentrated Marvel Comics live-action franchise has been reported by Hollywood Reporter as a primary motivation for the Star Trek franchise to try for a "reunification" of their television and film properties as well, broken up in the 2005/2005 "old" Viacom split.