Brown stink bugs are annoying, shield-shaped bugs that you can prevent from getting into your house and garden where they inflict mechanical injury to your seeds. They can also transmit yeast spot disease amongst your plants, and like their name implies, they can emit a gross, stinky chemical to ward off predators. While stink bugs aren't necessarily dangerous to you, they can do some damage to your garden. Plus, they stink. You certainly don't want them spending the winter in your house.
The best way to keep them out is to keep your doors and windows shut. Stink bugs are pretty big—nearly an inch long. Keep the cracks around your windows, doors, siding, utility pipes, chimneys, wood fascia and other openings sealed with a high quality silicone sealant or silicone latex caulk. Don't forget to also repair or replace any damaged screen doors or windows.
If you spot brown stink bugs in your garden during the summer, have a licensed pest control operator apply a synthetic pyrethroid to your yard. This could include deltamethrin, cyfluthrin, lambda cyhalothrin, cypermethrin, sumithrin or tralomethrin. If this isn't done by fall, the stink bugs will start moving into your house to keep warm over the winter. Unfortunately, these insecticides are broken down by sunlight and won't last more than a few days.
If the stink bugs are already in your house, try to figure out where they are getting in and seal up any cracks. You can vacuum the stink bugs up, but this will make your vacuum smell like stink bug. Don't use a pesticide inside of your house to kill the stink bugs. This will only result in carpet beetles moving in to feast on the carcasses, then on all of your woolens and stored dry goods. Then, in all likelihood, the stink bugs will return anyway and you will have a stink bug infestation and a carpet beetle infestation.