These modal verbs describe either possible actions (like can/could) or something that will occur in the future.
May and might are interchangeable, but only might is used when the event is imaginary
I may go to the movie tonight.
(There is a possibility of my going to a movie.)
I might throw this computer out the window.
(There is a possibility of me throwing this computer out the window)
If I had studied harder for the test, I might have received a passing score.
(I didn't study hard enough, so I didn't receive a passing score.)
When referring to the past, the verb “have" must be used in the construction.
She might have been taking a shower when you called.
They may have finished the exercise by now. I'll go and check.