This paper reviews some of our recent research on haptic exploration, perception and recognition of multidimensional objects. We begin by considering the nature of manual exploration in terms of the characteristics of various exploratory procedures (EPs) or stereotypical patterns of hand movements. Next, we explore their consequences for the sequence of EPs selected, for the relative cognitive salience of material versus geometric properties, and for dimensional integration. Finally, we discuss several applications of our research programme to the development of tangible graphics displays for the blind, autonomous and teleoperated haptic robotic systems, and food evaluation in the food industry.