Everyday remodel and cleanout debris is fine. The limits come from what the receiving landfill will accept and from how Arizona handles hazardous and special waste.
Hazardous waste, liquids, wet paint, solvents, fuel, and asbestos never go in a standard container. Surprise routes household hazardous material to periodic city collection events instead of a standing drop-off, so plan ahead if your project turns up old paint, pool chemicals, or pesticide.
Tires, medical waste, propane tanks, and appliances are also kept out of containers locally. The city classes appliances, tires, and batteries as special waste with their own handling route, so tell us about a water heater or an old refrigerator when you book rather than loading it.
Rock and concrete need a conversation. Local practice limits how much dense rubble can go into the larger container sizes, so a dedicated smaller container for block, slab, and landscape rock is usually both cheaper and easier to place.
Electronics should come out before loading too. If you're unsure where something belongs, ask your account manager before it goes in the container.