Years ago, I was making a stealth game in Unreal that I've since had to cancel amid circumstances beyond my control. At one point I was trying to make my characters' eyes nice, and the gold standard for that was (and arguably still is) Half-Life 2.
HL2 takes a novel approach: the eyes are not rotating sphere meshes with bones, they’re more-or-less flat planes with a shader on ‘em that makes 'em look like balls and points the iris/pupil where you tell it. The eye "plane" can be stretched as the eyelids open or close without affecting the visual, and you don't get any mesh intersection issues (which is why you've never seen the gman's eyeball push through his eyelid even though Gmod exists) or the uncanny appearance of rotating "with the head".
To get this right, I asked Valve's Ken Birdwell about how they got such a good sense of eye contact with this shader back in 2003. Here's the scoop:
