Most wood, drywall, roofing, flooring, cabinetry, and cleanout debris loads without trouble. The limits come from the city ordinance and from the facility that receives the load.
Yard trimmings have a firm rule here. The city makes it unlawful to mix yard trimmings with other municipal solid waste except as Georgia law allows, which in practice means grass, leaves, and limbs go in their own load rather than on top of a remodel.
The city's own collection rules also set out what the city and its contractor will not pick up: dangerous materials such as poisons, acids, caustics, infected materials, and explosives; unusual quantities of material from repair, excavation, or construction, including earth, plaster, mortar, and roofing; industrial process waste; and tree trimmings cut for pay. That last group is exactly why a project needs a container rather than the curb.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of a standard container with no exceptions. Tires, batteries, and electronics all need their own route as well.
Glass has a local quirk. Both drop-off sites take glass only when it is clean and by itself, with no bags, boxes, or other containers mixed in. If an item has you unsure, ask your account manager before it goes over the rail.