Antikythera mechanism is an ancient Greece machine excavated in 1900. The damaged remains and ingenious mechanical structure resulted in man's thirst to decode this mechanism. This paper reviews the historical development regarding reconstruction designs of Antikythera mechanism. The origin, the recovering process and the related historical records are introduced first. Available reconstruction designs, which are classified into the orientation of mechanism, the decoding of modern technology including the appearance, the functions of the exterior dials and the interior structure, other research and the authors' work are presented. Then, based on the viewpoint of mechanisms, the mechanism analysis of one feasible reconstruction design with the complete interior structure, by the authors, is presented. This new design to generate all known output functions also provides a possible embryo of Antikythera mechanism.