How much are we driven by hormones? How does this affect our notions of free will?

I don’t think we like to think that hormones affect our behavior, but it does. For example men can sense ovulating cues in women who are sexually fertile simply through the scent of sweat. From the study “Scent of a woman: men’s testosterone responses to olfactory ovulation cues.”:

Men exposed to the scent of an ovulating woman subsequently displayed higher levels of testosterone than did men exposed to the scent of a nonovulating woman or a control scent. Hence, olfactory cues signaling women’s levels of reproductive fertility were associated with specific endocrinological responses in men–responses that have been linked to sexual behavior and the initiation of romantic courtship.

So let us assume you’re at the gym, beach or bar, and you’re near an ovulating woman. Without knowing or wanting to, your testosterone might increase. From an evolutionary biology perspective, this totally makes sense.