For forwarders and carriers, UPS, FedEx, and DHL are the leaders in Express Freight. Most shippers (consignees and consignors) would refer to these companies as being international couriers.
Express freight is only cost-effective for small shipments. Moreover, each international courier has their own weight and size restrictions. Larger shipments will generally be cheaper to transport by air freight, and larger still by ocean freight.
Of all the shipping modes, shipping by an international courier is the most streamlined, in part because the shipment is completed by one company from pickup to drop-off.