The ability to lay eggs which mimic the host eggs is the key adaptation.

A female may remove a host egg before laying.

In Prestwichia aquatica, mating has been reported to occur prior to the emergence of females from the host eggs.

After emerging, females search rapidly for suitable host eggs by tapping their antennae over stems or barks of plants.

Metamorphosis occurs completely within the host egg.

Then, when she is ready to lay, she selects a nest, swoops down, removes a host egg, lays her own its place and flies off.

Parasitic cuckoos are often known to remove one of the host eggs before laying their own.

Most avian brood parasites will remove a host egg when they lay one of their own in a nest.

Some hosts do not exhibit egg rejection behavior and the cuckoo eggs look very dissimilar from the host eggs.

That left the problem of host eggs.