That's why I was shocked to learn that you can't burn just about anything in them. I knew this within reason but I was not aware that you couldn't burn your everyday household trash. Get our free mobile appIf you aren't entirely sure what you can and can't burn, just stick to firewood. The Minnesota DNR says burning of household trash has been illegal since 1969. In this case, those households are allowed to burn some household trash while following the proper guidelines.