Much ink and many electrons have been spilled in the last six months over whether Ronan Farrow is the son of Woody Allen, as everyone originally thought, or of Frank Sinatra, as his mother Mia Farrow hinted to Vanity Fair. (No I'm not going into the ramifications of the rest of the sad and sordid family saga - this is a straightforward genetics-genealogical essay.)
Yes, there is some resemblance between Ronan Farrow and Frank Sinatra, but not enough to be conclusive. On the other hand, he very strongly resembles his mother, and is the spitting image of her father, actor-writer-director John Farrow. (Mia Farrow takes strongly after her father also, as did several of her siblings.)
The phenomenon of "prepotency" is well known in genetics: the ability of one parent, often but not always the father, to stamp their characteristics on their offspring to the near exclusion of the other parent. The classic case in Hollywood is Alan Hale Sr. and Alan Hale Jr. - they looked so alike that to this day fans get confused as to which one was in what movie. (It was Jr. who was shipwrecked on Gilligan's Island, and Sr. who played Little John to both Fairbanks Sr.'s and Errol Flynn's Robin Hood.)
As to how brown-eyed Woody Allen could have had a blue-eyed son - brown eyes are dominant, blue eyes recessive. (It's not quite that simple, but it's a workable shorthand.) Recessive genes can skip one or several generations, reappearing when they find a match. (It's hard to tell, but based on Wild Man Blues, his mother may have had blue eyes.)
So yeah, Ronan Farrow may indeed be Woody Allen's son, but he is almost pure Farrow.