Cockroaches are nasty. They can survive a week with their heads cut off since the brain is in the middle of the body. They can also fly briefly which can be scary if they suddenly land on your lap, or face.
If they fly/crawl at you, best not to step or press them to death, just going to make a mess. Better lightly cup them in your hand and throw them against a wall quickly and hard. This way they'll get a concussion and just flip on their backs and you can sweep them up cleanly.