There is much speculation as to who the father of Rey, from "The Force Awakens", is. Several theories have already surfaced since the release of the movie. One of the theories is that Rey is related to Emperor Palpatine. The evidence behind this is the fact that she was left alone to wait on her family for her whole life. This theory states that her family is most likely dead and/or never coming back. This story would have been conjured up to keep Rey waiting for her family. It is believed that Luke abandoned her on this planet so that she would never leave and learn the ways of the force.
Another theory is that she is the daughter of Luke Skywalker. This would explain the look that he gives her at the end of the film. This would also explain how she is clearly so powerful with the force without any training. This would also make her the granddaughter of Darth Vader (Anikan Skywalker) who was also very strong with the force at a young age. This is supported by the theme music of Luke Skywalker playing when she battle Kylo Ren.
Rey could also be the daughter of Obi-Wan Kenobi. This would explain why Han and Luke look on her with a sort of hidden fondness. This would also explain her strength in the force.