They feed and reproduce on a variety of plants and are particularly damaging to fruit. You can cut cosmetic damage off fruit and still eat the rest of the fruit. To keep out stink bugs, cover vegetable plants with row covers. You can pick the bugs off plants and squish them or knock them off into soapy water. They are attracted to light and can get into homes where if vacuumed up, they can stink up your vacuum bag.
More Information: Brown Marmorated Stick Bug Pest Note