Sony Pictures has film rights to the character.
Marvel has owned Spider-Man since his inception. They do, and have always, owned Spider-Man.
If you’re asking about the film rights specifically, that’s more complicated.
Disney owns Marvel. Marvel owns the Spider-Man character. Every time
someone purchases a Spider-man backpack or lunchbox or T-shirt, Disney
is making money on that sale.
What Disney does not have are the film rights to the character. Sony
Pictures does. What this means is that Marvel Studios cannot just go
and create a Spider-Man film or have spider-Man appear in another film
by itself. They did negotiate a deal with Sony to allow Spider-Man to
appear in the Marvel Cinematic Films. That is why you see him in
Avengers: Infinity War, Captain America: Civil War, & Spider-Man:
Marvel had sold film rights for a number of its characters to various
studios over the years. Most of those have lapsed or returned to
Marvel Studios / Disney. If the acquisition of Fox is completed -
Spider-Man will be about the last major character that Disney/Marvel
does not have the film rights.
Beyond film rights, Marvel had sold the rights to their characters to
be used in theme parks to Universal Studios. The Universal Orlando has
a super hero land that includes a Spider-Man ride. Universal never
created similar lands or rides outside of Florida so the use of the
rights lapsed elsewhere. What this means is that Disney is free to use
Marvel characters in all of its theme parks EXCEPT the ones located in
Orlando. There’s an Iron Man ride in Hong Kong and a Guardians of the
Galaxy ride in California for example. The rules are a bit nuanced -
so EPCOT is getting a Guardians of the Galaxy ride, presumably because
the rights that Universal has are only for characters they already had
in use (so no Avengers, X-men, or Spider-Man). Universal can also only
use the comic book/cartoon versions of the characters. They do not
have rights to show Robert Downey, Jr as Iron Man in their theme park,