What are the causes of the muscles around your eyes to twitch?

Stress and strain. The most common form of muscle twitching is caused by stress. Tiny clumps of muscle cells become over-stimulated, creating small twitches that canbe seen under the skin of the eyelid. While not dangerous, it is annoying and few treatments are available. Rest, cool compresses, and artificial tears all help, but it usually runs its course in time.
Many things. This is usually called a "tic". Can be due to stress and anxiety. Could be due to medications. Sometimes, no cause is knowns. Certain seizure disorders could be the cause. If this has gone on for a long time of if there are associated symptoms, please see your pcp. You may need testing and possible referral. Usually, though, they are benign.