Predictive control of grasping forces when manipulating objects in the environment is suggested to reflect internal models that capture the causal relationship between actions and their consequences. The anatomical correlate of predictive control of grasping within the central nervous system is not completely understood. One structure which has been related to the neural representation of internal models is the cerebellum. Given its stereotyped cytoarchitecture, the widespread connections with cortical and subcortical sensory-motor structures and the neural activity of cerebellar Purkinje cells during sensory-motor tasks, the cerebellum has long been considered to play a major role in the establishment and maintenance of sensory-motor representations related to voluntary movement. Such representations are necessary to predict the consequences of our own movements. Here we review theoretical concepts, electrophysiological, imaging and behavioural data suggesting the cerebellum to be the anatomical and functional correlate of internal models relevant for predictive control of grasping.