There are several schools of thought on this. Personally, I think it completely depends on the degree you're talking about. For instance, it is possible to read a lie through someone's eyes (i. e. if they look to the left), and if you have read a lie, then you have read someone's thoughts in a sense, right? Furthermore, what someone does with their eyes can reveal attraction (i. e., if they blink at the same time as you, if they stare at your mouth, if their eyes look shy, all of these are signs).
So, basically, I don't believe that our eyes directly reveal our secrets, but I believe that their eyes can often reveal their emotions, and if you watch their eyes while in a conversation with them, it might reveal their emotions, too. However, note that it is much easier to figure people out by other mannerisms.