One of my Madagascar Giant Day Geckos (Phelsuma madagascariensis grandis) laid eggs overnight and started off the breeding season 2013 for my reptile collection (in case you didn't know, I like reptiles and have a few of them). Day Geckos have a fascinating mechanism of egg laying! They usually lay in clutches of two and their eggs are calcified. However when the eggs first are laid they are soft and pliable because the egg hasn't hardened yet. These Geckos live up in trees and lay one egg a time into their hind feet and then roll the egg to give it its round shape, after which they attach it to something, usually hiding the egg in a sheltered place.
Not necessarily a new biomimetic hot topic, but what if we could utilize artificially created calcium eggs? Think of Jurassic Park (Big Reptiles!!!), though unless you read the book you won't get my reference (the movie sucks, sorry)