We view origami as the machinery of geometric construction and study the formal models of origami . Origami successively transforms geometric objects by a set of fold rules. As in symbolic and numeric computation, in geometric construction by origami, we have a number of approaches to look into the process of the transformations. We give the overview of our research activities of abstracting origami as a model of computation, as part of the development of a computational origami system called Eos. In particular, we discuss the computation model that led to the design of an origami language for specifying the construction of origami.