Introduction Folding and unfolding is an exciting area of computational geometry.
It is attractive in the way that problems and even results can be easily understood, with little knowledge of mathematics or computer science, yet the solutions are difficult and have involved many sophisticated techniques. In particular, we are interested in efficient algorithms for characterizing foldability, and finding efficient folding processes, or in proving that such algorithms are impossible. In the last few years, there has been tremendous progress on many of the fundamental problems in folding and unfolding, yet some of the most important questions still remain open. This is what makes the state of the area so exciting. Many results in folding and unfolding can be characterized in the following way.