Most construction and household debris is fine to load. The limits come from Illinois disposal law and from what the receiving landfill accepts.
Illinois EPA states that state law prohibits landfilling many common electronic items, including televisions and computers, and that state law bans the landfilling of used or waste tires, which have to go to a permitted tire facility instead. Lead-acid batteries, used oil, and liquid waste stay out as well, and landscape waste has its own route.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos never go in a standard container. Asbestos in an older DeKalb property needs a licensed abatement route before any demolition starts.
The City's own list of material its collection program will not take is a useful guide to what to flag when you book: radioactive material, liquid waste, acids, caustics, drums, lead-acid batteries, explosives, hot ashes, stone or brick material, dirt, and motor vehicle parts including tires, engines, seats, radiators, and fuel tanks.
Clean concrete, brick, and asphalt are accepted in a container, and they usually cost less to handle when kept in a load of their own rather than mixed with wood and drywall.
If you are unsure about an item, ask your account manager before it goes in.