It shouldn't come as a surprise to learn that Marc Webb, the director of the first two Amazing Spider-Man movies, will be back to direct the third. The film is current being written by Alex Kurtzman, Roberto Orci, and Jeff Pinkner.
So far I'm completely satisfied with what Webb has done with this franchise, and it's great that he's still going to be at the helm bringing us awesome Spider-Man stories and characters.
Andrew Garfield and Paul Giamatti are both set to reprise their roles in a third movie. We don't know who else will return, so I guess we'll just have to wait and see who's still standing at the end of The Amazing Spider-Man 2.
The Amazing Spider-Man 3 is set to be released on June 10th, 2016. Sony Pictures has a fourth film planned that will be released on May 4th, 2018, and they also are planning some villain spin-off movies that will include Venom.