Grinding your teeth or clenching your jaws is known as bruxism.  It often happens as we sleep, caused not just by stress and anxiety but by sleep disorders, an abnormal bite, or teeth that are missing or crooked.  Symptoms include a dull headache or a sore jaw.  You could have teeth that are painful or loose from severe grinding.  This can lead to fractures in your teeth.  Your dentist can fit you with a mouth guard to protect your teeth during sleep.