When living in a foreign country (in my case Australia), without a place at your residence to receive parcels you often have an option to get a parcel locker from the post office. However, the parcel locker in many other countries (in my case Australia) only accepts packages from which the final delivery is done through the "national Post network." The problem is that it is hard to find which couriers in my country of origin will end up using the national post network for the final destination where the package will arrive. I would like to inform relatives in my home country to advise them which couriers to choose based on this.
Generally, absent a special agreement with the shipping company or unusual circumstances, only postal organisations can deliver to post office boxes (and their associated parcel lockers). This is the case in almost all of the world.
In particular, Australia Post state that: "We'll accept domestic and international parcels from other carriers as long as they've paid to send them via the Australia Post network." For national postal organisations this is handled through the UPU. I was not able to locate any private carrier which had actually made this arrangement. I did, however, locate individuals who said that UPS, FedEx and DHL all could not deliver to an Australia Post PO box.
This means that if you ship via a country's national postal service, such as the United States Postal Service, they can deliver to your Australia Post PO box. However, if you ship via a private non-postal service such as UPS, FedEx or DHL, they cannot deliver to PO boxes.
If you are shipping from the US to an Australia Post PO box, you will need to ship via the United States Postal Service. Happily, this is usually the least expensive international shipping option, and from my experience tends to clear customs more easily and quickly. (To save even more, buy and print your postage and customs form online.)
Note that if you do ship to a street address, any carrier will do. If you haven't got a safe place for the carrier to leave your package, they will be able to hold the package in their nearest distribution centre for you to pick up.