Ever since the new characters in Star Wars were revealed, there's been speculation as to their past, there's been Finn Calrissian, son of legendary Lando Calrissian and Rey Solo, daughter of Han Solo. However we now know that are unlikely true but have not been fully disproved as yet.
Finn was conscripted into the First Order from a very young age and was only known by his FN-2187 until he freed Poe Dameron who rewarded the stormtrooper deserter with the nickname of Finn. Its unlikely that he was ever connected to Lando in anyway apart from possibly hailing from the same planet as him and I'm not talking about the gas giant of Bespin. Also he could be a relative of Mace Windu given his light sabre skills or at least his attempt at them. Whereas the original trilogy was father vs son, this new trilogy could be about grandchildren.
Most speculation on Rey's background has been on Luke Skywalker and the Solos (Han Solo and his wife Princess Leia). If Rey was a child of one of those three, she would therefore be related directly to (sister) or closely related (cousin) to Ben Solo, aka Kylo Ren. If Rey was a Solo why was she deserted on Jakku? However, there's a new theory in that she is the daughter or granddaughter of Palpatine, the Emperor who oversaw the Galactic Empire. At the end of Star Wars - The Force Awakens, both Luke and Rey stared one another out in the last shot of the film, it could be that he knew who she was. If she was Luke's daughter, where's Mara-Jade who in the expanded universe is Luke's wife. Why would Luke hide his daughter and then go away from her, why not hide with her?
Palpatine theory is a possibility, although in the films, he isn't seen to have a wife or a relation but that doesn't mean he didn't have a secret wife or girlfriend. There are rumours that he could have caused the virgin birth of Anakin Skywalker by trying to experiment with midi-chlorins when Palpatine visited Tatooine. A relation of Palpatine would definitely be a twist.