Last but not least: the documentation pack. When I send a design out, the pack contains literally everything necessary to produce the design. This includes a master assembly drawingmaster assembly drawing, a master PCB fabrication drawing (which contains information not in the gerber / ODB++ electronic data), drill drawings, test requirements, test methods with pass fail criteria, schematics (if you want the CEM to troubleshoot failed items), full production BoM (with all non populated parts removed).
Clearly, gerber / ODB++ data is sent as well (all the stuff necessary for the fabrication to be done). ODB++ is the preferred method for the better assemblers as of 2018.