In this thesis, I present an exposition of origami constructible objects and their associated algebraic fields. I first review the basic definitions and theorems of field theory that are relevant and discuss the more commonly known straightedge and compass constructions. Next, I introduce what origami is and discuss the basic single-fold operations of origami. Using the set of single-fold operations, I explain what it means for an object to be origami-constructible and show how to prove or disprove the constructibility of some origami objects. Finally, I present extensions of origami theory in literature and pose some additional questions for future studies.