Glance: to give a rapid look.
Glance at/over/through/round = take a quick look.
She had glanced shyly at him from behind her fan.
He glanced at his watch / the clock / shop windows.
I glanced round the room before I left. (to check that nothing was missing)
She glanced down the list of names.
Glance over / through a letter.
Glance oneīs eye down / over / through, etc. = to give a hurried reading or look.
He glanced his eye over the titles of the articles.
Glimpse: to see something or someone by chance for a very short time.
Catch a glimpse of (more common than the verb glimpse)
I canīt describe him well, I only caught a glimpse of him as he drove off.
She caught a sudden glimpse of herself in the mirror.
I glimpsed someone behind the curtain.
Eye somebody up: to look at someone in a way that shows you think they are sexually attractive.
There was a group of lads at the bar, eyeing up every girl who walked in.