Rear View Mirrors

On my passenger side rear view mirror, the actual glass has separated from the backing plate thing. What is used to hold the glass to the back? My glass is just sitting loose in it now. Also, my driver side mirror recently became a little wobbly. Would just reseating the mirror make it harder to move around?

We use a 2 part epoxy mixture to attach the mirror back on. Simple to do. If you look closely at the back of the glass, you will see a silicone looking paste that was original. Clean it off good and glue back on.