If you grow Rhododendrons or yews, you may have encountered the damage caused by the adult of the black vine weevil. Due to the shape of their mouthparts, these night feeding pests leave what is described as a "half-moon" notch at the edge of the leaves. It is very distinctive and it may do the same type of feeding damage to hostas.

For woody plants, the more significant damage is done by the larvae of these insects feeding on the roots. That is why the major control measures for this insect are to treat the soil around the plants.

If these are bothering your hostas, check other nearby shrubs and see if they are being damaged too. If so, you may need to treat them to control the problem. A non-chemical alternative would be to go out at night with a flash light to see if you can catch the adult. Be sure to alert your neighbors about what you are doing poking around in the dark.