Rey's father is still a mystery, but there are some clues in The Last Jedi that might give us a hint. In the movie, Kylo Ren tells Rey that her parents were nobodies and that she should embrace the dark side with him. However, later on we find out that Luke was trying to teach Rey how to use the Force before he disappeared. This could mean that Rey's father is someone who is strong with the Force, which would make sense given her own abilities.
There are also theories that Rey's father is Obi-Wan Kenobi, which would explain why she was drawn to his lightsaber in The Force Awakens. It's possible that Obi-Wan hid Rey on Jakku to keep her safe from the First Order, and if this is true then it would mean that Luke and Leia are her uncle and aunt respectively.
Whoever Rey's father may be, we'll have to wait for future movies to find out for sure. In the meantime, we can just enjoy speculating about this intriguing character!