That sounds like fungus gnats.

Eventually, they'll kill the plants by feeding on the roots.

Fungus gnats (AKA soil gnats) can be difficult to get rid of. They live in moist (overwatered) soil or growing mix. I've had them, and some of my plants/pots recovered after treatment with a mixture of 1 part neem oil (concentrate), 1 part hydrogen peroxide (3% solution, from drug store or dollar store) and 3 parts water. Dusting the surface of the soil/mix with cinnamon powder also helps. It takes several weeks to rid my pots of the gnats. Treating the soil/mix is to kill the grubs/larvae.

Yellow sticky traps can capture/remove the adults as well, and can help eliminate the gnats. You can buy traps, or make your own with bright yellow index cards and honey.

Are they little flies? Or white insects that mostly sit on the plants?