Most construction and household debris is fine to load. The limits come from Illinois disposal law and from what the receiving landfill will take.
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 must go to a permitted tire facility. Lead-acid batteries, used oil, and liquid waste are kept 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 Elmhurst house needs a licensed abatement route before demolition work starts.
The City keeps construction debris out of its own collection stream entirely, and says so in its code: brick, concrete, plaster, soil, stumps, and waste from building construction, alterations, excavation, or repair must be removed at the owner's or contractor's own expense, and it is not the City's duty to collect any of it. A container is the usual answer, and that is why.
Clean concrete, brick, and asphalt do go in a container, and they are often cheaper to handle when kept in a single-material load rather than mixed with wood and drywall.
Ask your account manager about anything you are unsure of before it goes in.