Star Wars: The Force Awakens, what is the connection Between Rey and Luke Skywalker? Are they related?
Well, there are speculations that Rey is Luke's daughter... You might be able to infer it from how strong Rey is with the force. In the trailer, Luke says that the force runs strong in his family: His father, his sister, and himself. And he seems to be talking to someone, saying it runs in him/her as well. That's why Kylo Ren was so strong: because of Leia.
Also, in the movie, Maz had Luke's lightsaber in her keeping, and it called to Rey, when it has never done that for anyone before. When this was found out, Maz also explained to Rey that what she was looking for was not in the past, on Jakku, where someone had 'abandoned' her as a child. Instead, it was in the future. And since Maz wanted her to help find Luke, that might have been a hint that Rey is Luke's daughter.
It is also very possible if you take into account the plot around Kylo Ren, aka Ben Solo. His mom is Leia Organa, which means his uncle and ex-mentor is Luke. So, in the interest of plot development and storyline, it would be pretty ironic to see Kylo Ren face off against his cousin, who will probably be Luke's new apprentice. It could be a throwback to when Anakin, Obi-Wan's old apprentice, faced off against Luke, Obi-Wan's last apprentice.
Another possible point, many have marked the similarity between Jakku, and Luke and Anakin's home planet, Tatooine. So... Hehehe you can draw your own conclusions...
But watching the trailer and the movie, especially where it is purposely not mentioned who left Rey on Jakku, that this particular connection is not one that will be made so soon. However, and this is my personal take, if the Moviemakers are smart, they would have dropped all these hints on purpose to make everyone think Rey is Luke's daughter. But at the same time, they would have come up with a totally different, yet plausible explanation, that will blow us all away. If they're smart.