Most of what comes out of a remodel or a cleanout is fine. The limits come from Illinois law and from what the receiving landfill will take at the gate.
The Illinois Environmental Protection Agency keeps several things out of landfills statewide. Yard and landscape waste has been barred since 1990, and so have lead acid vehicle batteries. Large appliances, which the state calls white goods, can't be buried unless their refrigerant, mercury switches, and other components have been pulled first. Liquid used motor oil has been out since 1996.
Electronics are the one that catches people out. Illinois bans covered electronics from landfills, and the state's list is long: televisions, monitors, computers, tablets, printers, scanners, game consoles, speakers, stereos, keyboards, and more. The ban covers businesses and job sites, not just households, so one old monitor tossed in the container can create a problem for the whole load.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are out of a standard container too. Tires and appliances usually need to be handled separately and billed per piece.
If you have something in that gray area, ask your account manager before it goes in. One question beforehand is cheaper than a rejected load.