Aizawa Is Izuku's Uncle - My Hero Academia Theory

Other than Izuku's mom, My Hero Academia fans don't know too much about Izuku's family. According to Tumblr user neubauje, we may have already met one of his relatives: his homeroom teacher, Shota Aizawa.

Aizawa's primary quirk is Erasure, which allows him to temporarily disable other people's quirks. However, he also demonstrates some light telekinetic ability, which he uses when he does things like weaponize his scarf. Inko Midoriya, Izuku's mom, also possesses mild telekinetic abilities. 

Neubauje speculates this is because they're siblings. Specifically, Aizawa's father possessed powerful telekinetic abilities but deliberately sought out someone with a quirk-canceling ability in the hopes of combining those powers in his children.

In Inko's case, her powers were unimpressive because her mom's quirk-canceling ability actually inhibited her quirk development, but Aizawa inherits them both. The quirk-canceling is also why Izuku is born quirkless; her canceling genes prevent him from inheriting either her telekinetic abilities or the fire quirk his father supposedly had. 

All For One Is Izuku's Father - My Hero Academia Theory

There's some pretty strong evidence to suggest that All For One, the main villain of the series, might be Izuku's father. Shigaraki Tomura, All For One's protege, is the grandchild of the woman who trained All Might and passed his powers onto him. It stands to reason that Izuku, All Might's mentee, might also have some kind of connection to All For One.

What's more, All For One had a younger brother who was apparently born quirkless - something Izuku could have inherited if All For One were his dad. 

My Hero Academia also makes liberal use of Star Wars references. All For One is likely influenced by Darth Vader, both because of their vast and powerful influence over a villainous organization, and because of the signature headgear that supplies them with oxygen and hides their disfigured appearance. Following this theme, All For One might one day face Izuku in combat and utter a version of Vader's famous line: "Izuku, I am your father."