A masticatory robot refers to a robot that can perform at least some defined human masticatory function. This chapter briefly reviews the masticatory system, masticatory measurements and computational models of mastication that are relevant to masticatory robotics. Also critically reviewed, is state-of-the-art in robotics research with respect to the engineering of the human jaw system. The masticatory system has two rigid components: a fixed maxilla (upper jaw) and a mobile mandibular (lower jaw). These are joined by two temporomandibular joints (TMJ). Unique features of the TMJ are described. The muscles of mastication are explained with regards to their role in the rhythmic opening and closing of the mandible in three-dimensional (3D) space. Because the breakdown of foods is performed directly by the teeth; the functionalities of the incisors, premolars and rear molars are presented. Two computational models of the masticatory system are presented in which Hill-type muscle models are used. We also describe masticatory robots developed for dental training, jaw simulation, food texture and breakdown analysis, speech therapy with regard to muscle modelling, TMJ models, masticatory biomechanics and controls of actuation. Finally, we discuss the major accomplishments and challenges in masticatory modelling and robotics; and we compare a number of such robots in light of relevant biomechanical aspects of the mastication system. The application of artificial intelligence in robotic mastication is also described briefly.