Ordinary construction and cleanout debris is fine. The limits come from Illinois law and from the landfill that takes the load.
Illinois bans a long list of electronics from landfill disposal, covering televisions, monitors, computers, tablets, printers, scanners, game consoles, and home audio equipment, for businesses as well as households. A single screen can get a whole load rejected at the gate, so pull them before you load.
The state also keeps landscape waste, used tires, lead-acid batteries, used motor oil, and appliances that still hold refrigerant out of landfills. Each of those needs its own outlet.
Hazardous material is out of a standard roll-off everywhere: paint, solvents, fuel, antifreeze, pesticides, pool chemicals, and anything corrosive or flammable. Liquids, asbestos, and medical waste can't go in either.
One local wrinkle is worth knowing. A container permitted in the O'Fallon right of way may be used only for garbage or refuse, as the Illinois vehicle rules define those words. A street container being used for something else falls outside the permit. If you're not sure how an item is classified, check with your account manager before it goes in.