Continuous adjustment appliances are provided that can store a large number of geometries that can be successively accessed throughout orthodontic treatment, with each geometry can correspond to an arrangement of the patient's teeth. An appliance according to the present disclosure can be stimulated to transition among the myriad geometries, which can include changes to the overall shape of the appliance as well as the position and geometry of the cavities corresponding to a patient's teeth. Methods of creating the continuous adjustment appliances and methods of treatment using the continuous adjustment appliances are also revealed.