We report on recent work in modelling the process of grasping and active touch by natural and artificial hands. Starting from observations made in human hands about the correlation of degrees of freedom in patterns of more frequent use (postural synergies), we consider the implications of a geometrical model accounting for such data, which is applicable to the pre-grasping phase occurring when shaping the hand before actual contact with the grasped object. To extend applicability of the synergy model to study force distribution in the actual grasp, we introduce a modified model including the mechanical compliance of the hand's musculotendinous system. Numerical results obtained by this model indicate that the same principal synergies observed from pre-grasp postural data are also fundamental in achieving proper grasp force distribution. To illustrate the concept of synergies in the dual domain of haptic sensing, we provide a review of models of how the complexity and heterogeneity of sensory information from touch can be harnessed in simplified, tractable abstractions. These abstractions are amenable to fast processing to enable quick reflexes as well as elaboration of high-level percepts. Applications of the synergy model to the design and control of artificial hands and tactile sensors are illustrated.