The Eee PC 1015P seems to be a refresh of the existing 1005P, with a similar matte display, chiclet-style keyboard, webcam, and signature. It now features a larger touchpad and has a battery life of up to 14 hours with wireless disabled.
An image of the 1016P isn't available, so it's difficult to say exactly what to expect. Blogeee.net says it will be business-oriented to compete with notebooks from Lenovo and others. It too has an aluminum hull and a 14-hour run time.
The 1018P is reportedly Asus' thinnest netbook to date, measuring only 18mm thick. Known features include a 10-hour battery life, an integrated fingerprint scanner, and USB 3.0. Prices and availability aren't available yet, but more information should surface next week.