they are called spider mites..... you will see their eggs under your leaves, I adult will lay 100 eggs and literally eat and kill your plants.
Depending on how bad the situation is spray your plants with neem oil (using directions that come with it).... this is a pretty soft and natural way of getting rid of them or at least keeping them at bay. On a real serious outbreak, get a can of fogger and set it up in the affected room. Always follow directions closely. This procedure needs to be repeated 4 days after the first apllication, and then maybe every 10 days. I doubt you'll ever get rid of them completely for any length of time.

Good luck!