Boisea trivittatus found east of the Rocky's in North America, boxelder bugs are about 1/2" long with black bodies with red markings on their backs. They feed on seeds of boxelder, maple and ash trees. Check out this photo below from the University of Minnesota Extension Office.
Though they feed primarily on seeds, they may suck the juices from leaf material but have not been known to cause severe or lasting damage.
You may find them gathering on the south facing walls of your home and once the weather cools down they may invade homes or hide in walls or under siding. For this reason, people call them pests, but they are not really doing any damage.
Boxelder bugs are related to stinkbugs, although they do not have the same type of stink gland. They do have defensive chemicals in their leg joints that may stain a surface if the bug is squished.
If you notice an abundance of boxelder bugs in your yard, not to worry, they won't harm your plants. Their natural predators will take care of the over population in many cases. If you get a few in your house, hand pick them and flush them down the toilet or suck them up with a vacuum cleaner. I do not recommend using pesticides as you will be destroying potentially good bugs in the process and exposing your family and pets to nasty chemicals. If you do decide to use a chemical on them, only spray directly on the boxelder bugs and follow the directions on the package to the letter. Do not spray all around your home if you don't see them; the chemicals only work if sprayed directly on the bug. You can also try a homemade bug spray directly on the bugs. The recipe is as follows:
Homemade Bug Spray
Mix the two ingredients well and do a test spray on nearby plants if you will need to spray plant material. Wait 24 hours and check to see how the plant looks. If it looks wilted or sickly do not spray any more on your plants. Some plants may be more sensitive than others. Water the affected plants to help wash off the soap.
Spray the soapy solution directly on the bugs, as spraying where the bugs aren't will not work.
To prevent them from getting in your home, seal up any cracks you might have around your windows, doors and siding. Repair screens and soffit vents and install door sweeps on exterior doors. Not only will this prevent bugs from getting in, but it should help with heat or cold loss as well.
Boxelder bugs are not a pest and should be left alone for the most part. Keeping nature in balance is important so unless you have a severe infestation in or around your home, it's best to leave these little guys alone.