In this paper we consider a particular technique for achieving dexterity in manipulation with robot hands, which intentionally exploits rolling contacts. We report in some detail on modelling rolling contacts, and provide a result on the analysis of controllability of rolling pairs of bodies, which serves as a theoretical basis for the exploitation of rolling for dexterity enhancement. We conclude by illustrating some aspects of the problem that could not be touched upon in the paper, and open problems that still remain to be solved.