This idiom is used when describing the way a situation appears, while allowing for the possibility that things may be different:
On the face of it, the company looks very profitable. (The company appears to be very profitable, but this may not be the case.)
(UK) Someone who's on the nod is either asleep or falling asleep, especially when the shouldn't or are are in a position unusual for sleep, like sitting or standing.
If someone is very annoying and always disturbing you, they are a pain in the neck.
Pain in the butt, or pain in the ass (USA), and Pain in the arse (UK) are less polite alternative forms.
When someone is wearing a plastic smile, they are appear to be happier with a situation or events than they actually are. This is actually a description of the forced smile you might see in many photographs.
If someone wants their pound of flesh, the force someone to pay or give back something owed, even though they don't need it and it will cause the other person a lot of difficulty.
If you put on a brave face, or put a brave face on something, you behave confidently or cheerfully even though things are difficult. ('Brave front' is also used.)
If you rack your brain, you think very hard when trying to remember something or think hard to solve a problem, findf and answer, etc. ('Rack your brains' is an alternative.)