"The Amazing Spider-Man" is not a continuation, or a prequel, it is a remake. It's produced by Sony, rather than Warner Bros., and based on the final scene, it's safe to assume they will release another version of the second and third.
It is hard not to compare "The Amazing Spider-Man" to "Spider-Man," the blockbuster that set off a chain of superhero franchises in the early 2000s. Normally, a remake happens when a new generation (and new target audience) emerges 20 or 30 years later, with brand-new styles or technologies; the Tobey McGuire film (although before the 3-D era) is hardly irrelevant. But this is Hollywood, enough said.
We meet Peter Parker as a boy. His father is a genetic scientist working on a formula to splice human genes with other species that are able to regenerate broken limbs. He stumbles on an idea that he decides is too dangerous to share, drops his son off at his aunt and uncle's house and flees with his wife. Flash forward to a 17-year-old Parker (Andrew Garfield), preoccupied with photography, skateboarding and science, because what adolescent isn't obsessed with algorithms?
His father's old briefcase leads him to his old partner, Dr. Curt Connors, head of genetic science at the multinational Oscorp. He sneaks into an intern group, where he catches the eye of both Connors and his classmate Gwen Stacy (Emma Stone), the replacement for Mary Jane.
The 136-minute film spends a lot of attention setting up a number of stories -- the beginning of the love story between Peter and Gwen, Peter's anger over his abandonment, his loneliness and bullying; it also spends a fair amount of time setting up the genetic science that will eventually turn Dr. Connors into The Lizard, a half-rat half-reptile bent on changing the human species.
It is a film that takes itself much more seriously than the original. What Warner Bros. produced was an over-the-top action film that bordered between incredible adventure and pulp-like cheesiness. What Sony has created is incredible adventure mixed with science and conspiracy theory.
Watching the film in 3-D is enough to keep us interested for one remake, but Sony is going to have to think a little harder when remaking the next few sequels.