I just can't find it. What if an enemy deals more damage to one of my meatshields than it can take? Does the excess damage just not happen?

Generally it just means he's deader. I say generally because there are a few baddies out there that penalize you for excess damage. The Hill Troll in Journey Down the Anduin converts excess damage to threat for example.

Edit: Crap. I thought I was on the LOTR forum. Above is completely wrong.

Ah ok, thnx for the info!

With threat you mean doom or something special? Don't tell me details if it's special, I'm only learning with act 1.

Page 7 of the rules reference under Dealing Damage/Horror

"When an investigator is dealt damage or horror, that investigator may assign it to eligible asset cards he or she controls. To be eligible, an asset card must have health in order to be assigned damage, and it must have sanity in order to be assigned horror."

"An asset cannot be assigned damage beyond the amount of damage it would take to defeat the card, and cannot be assigned horror beyond the amount of horror it would take to defeat the card."

"All damage/horror that cannot be assigned to an asset must be assigned to the investigator."

Sorry, please ignore what I said. netherspirit is completely right.

Ooooh ok, that makes that big guy a lot harder to stand up against ... thnx.

You can, however, split up the damage between yourself and your assets. If you're about to take three damage, and you've got a Research Librarian and a Bulletproof Vest in play, you could assign one point to the Librarian, one to the Vest, and one to yourself. You just couldn't assign two damage to the Librarian, since one point is enough to finish him off.