Normal building debris and household junk are fine. The limits come from Illinois rules and from what the receiving facilities will take.
Illinois keeps yard waste out of regular trash and landfills, so grass, leaves, and brush have to be handled on their own. The city runs a brush program for that, and it will reject limbs over six inches across, root balls, lumber, fence posts, and anything that arrives in a container. Batteries also have a separate route now that Illinois requires free collection points for them, so they should never ride along in a dumpster.
Hazardous waste, liquids, paint, solvents, fuel, used oil, and asbestos cannot go in a standard container anywhere in the state.
Electronics and tires are handled separately as well. DuPage County keeps a list of drop-off locations for televisions, monitors, computers, and small appliances, and that is the right path for them.
One more thing is useful to know. Clean concrete, brick, and asphalt are treated as a different material from mixed debris in Illinois, so keeping a clean load clean can change what disposal costs. Ask your account manager how to split the material before you start loading.