Tim Bowen really has an eye for spotting a good idiom with this article.
Parts of the body are a rich source of idioms but the one that seems to feature most frequently is eye, probably because it can act as a synonym for the very common verbs look, watch and see. Someone may ask you to run (or cast) your eye(s) over something (meaning to read or look at it very quickly) or they make ask you to keep an eye on someone or something (look after a person or a thing). You might have your eye on something (to have seen it and want to have it or buy it) or you might have an eye for something (have a natural ability for seeing or finding something, as in 'She has a good eye for detail').
You could go into some situations with your eyes open (knowing there could be many problems, as in 'I went into the job with my eyes open') and, in others, you might be able to do things with your eyes closed (very easily). Of course there is often more to something than meets the eye (it is more complicated than it seems) and, in some situations, you may need eyes in the back of your head (to be able to notice everything that is happening around you). If you are very busy, you are up to your eyes in work, even though you might have one eye on the clock (keep looking at or paying attention to something while you are doing something else).
One day someone might catch your eye (attract your attention) and you might find that you can’t take your eyes off them (you are unable to stop looking at them), especially if you only have eyes for them (like or love them and no-one else).