To start, there is a scene in the movie where Rey is called to a spot in a basement that contains Luke Skywalker's lightsaber. When she grabs it, she has a vision that hints at events in hers and other characters in the movie in the 30 year gap between Return of the Jedi and A New Hope. During those flashes she hears voices. If you listen carefully you can hear the voice of Obi-Wan Kenobi and Yoda. More interesting is Ewan McGregor and Frank Oz reprised their roles just for that brief sequence. The last line in the sequence "Rey" was actually spoke by Alec Guiness using a little sound manipulation of him saying the word "afraid". You can read more from Abrams geeking out over the voices at Entertainment Weekly.
THR made an interesting note of a line in the movie which suggests that Stormtroopers have been clones all along. In the movie it was suggested that maybe using a clone army was better after the betrayal of Finn who was kidnapped and trained by the First Order as a child. Until that line, it has been assumed by fandom that the use of clones was abandoned by the Empire by the time of Star Wars: A New Hope. In the (now defunct) extended universe, they were all humans as Emperor Palpatine didn't particularly like aliens. In the Luke movies, it was just never referenced. As the article points out, "By establishing that Stormtroopers are factory-created drones, they become little more than robots, making the high kill-rate of our heroes somewhat less objectionable. It "cleans up" their record, and, in many ways, sanitizes the war of the franchise's title." That probably wasn't the intention but Abrams has found canon to be shackle (hence eliminating the EU) and more than likely it was just a way of explaining the existence of Finn who had to be a "bad guy" to become the good guy mostly to explain away the finale act of the film. The reference was also just a nod to previous films and nothing more. Still the unintended side effect is a bit of sanitizing the heroes of the Star Wars trilogy.
In another story beat, R2-D2 has an appearance in the movie but to start he has been essentially powered down for 30 years waiting for Luke Skywalker to return. In an interview with Abrams and they writers, they explain his late appearance was apparently an attempt at delayed gratification for the audience and to have a little emotional balance for the audience with the return of one character after the loss of another. He also provided the key information to find Luke, which apparently was part of his download of the Death Star database way back in A New Hope (that download was obliquely referenced by Kylo Ren apparently).
Another story beat is hinted at in the trailer and not really explained at all in the movie which is what is motivating Kylo Ren (aka...well his real name is too spoilery). Basically he idolizes Darth Vader (not Anakin) and his goals (which were never clear in the movies) and complete whatever those goals were. Really it seemed more like Kylo Ren himself is very weak in the force and latched onto someone that represented strength but that is just my take.
The biggest story beat of all and major spoiler, is the death of Han Solo. THR has an interesting article on why it works and why it is necessary but what it comes down to is its a way to pass of the torch from previous generation to next generation with sufficient dramatic weight and sets Kylo Ren as the new big bad to fans. There is also an argument that this is a lazy way of doing both things. Personally I think its more simple than that - Harrison Ford dictated it as a condition of returning to the role. He had said for decades now that he thought Han should have died during Return of the Jedi. JJ Abrams supported THR's theory in an interview when he said "“Long before we had this title, the idea of The Force Awakens was that this would become the evolution of not just a hero, but a villain. And not a villain who was the finished, ready-made villain, but someone who was in process. ...Star Wars had the greatest villain in cinema history. So, how you bring a new villain into that world is a very tricky thing. We knew we needed to do something fucking bold. The only reason why Kylo Ren has any hope of being a worthy successor is because we lose one of the most beloved characters."
I am on the fence about writing a review as I found the movie deeply flawed. Entertaining, a good homage to Star Wars but as an exercise in storytelling it just not that good that just wastes an epic ton of potential. At almost all levels, calling it Star Wars: A New Hope re-made isn't an exaggeration as it retreads almost all the story goalposts of that movie with a touch of Empire and Jedi mixed in. On top of that the new characters are all of very one dimensional. The worst offender just might be Rey. In the video below Max Landis (Chronicle) calls her a "Mary Sue" in the video below. A Mary (or Marty) Sue is a reference to a fanfic story that inserts a superior character into existing franchises that is for all intents and purposes perfect from the beginning and the story is just about discovering those perfections. Landis makes a pretty convincing argument that Rey is a Mary Sue but be warned this video is chock full of spoilers.