[Boogieman]

“This begs the question, is Tyrion the son of a Targaryen, instead of Tywin Lannister’s child?”

There’s a longstanding theory that Tyrion is the bastard son of Joanna Lannister (Tywin’s wife) and Aerys Targaryen (Dany’s father). Apparently Aerys had a thing for her, and we know that Tywin repeatedly said he didn’t believe that Tyrion was his son, he just couldn’t prove it.

Also, all the Lannisters generally have blonde hair, especially the children of two Lannisters. Tywin and Joanna were both Lannisters, they were cousins. Just like Jaime and Cersei, we would expect all their kids to have blonde hair, but Tyrion has blonde hair streaked with black, so that is another clue that he could be a bastard.

[TexasFreeper2009]

Good catch!

You could be right.

[drjimmy]

There’s a longstanding theory that Tyrion is the bastard son of Joanna Lannister (Tywin’s wife) and Aerys Targaryen (Dany’s father).

That would give an additional meaning to the title of the penultimate episode. While "Battle of the Bastards" refers to Jon Snow facing off against Ramsay Bolton, Tyrion was also involved in a battle, in Meereen.

In season one, Tyrion says to Bran, "I have a tender spot in my heart for cripples and bastards and broken things." I assume he was thinking of himself as a broken thing, but he might have unknowingly been talking about his bastard origins as well.

[ChiefJayStrongbow]

... and mismatched eyes. One of his eyes is purple, which is the color of Targaryen eyes.