Haptic perception refers to the perception one has of one's body, and of attachments to it, by means of sensors in the body. The term incorporates what is commonly meant by `touch,` and more besides. For example, without benefit of vision one is aware of the positions of one's limbs, and one can also ascertain properties of objects (e.g., weight, length)by wielding and hefting them. These aspects of haptic perception, referred to as dynamic touch, have their basis in receptors that sense the states of muscles and tendons. Unlike vision and audition, whose importance to everyday activity are obvious, the haptic perceptual system is strikingly subtle in its contribution to our everyday achievements of perceiving and acting. The fact that the loss of the sense of touch (without concomitant paralysis) is extremely rare and profoundly devastating begins to illustrate the fundamental importance of this sense in common activities such as lifting a cup, using a pen, pointing to a word, or just standing upright. Our research is directed at dynamic touch and an understanding of the role it plays in everyday controlled manipulations. We ask, What can it do?; and, How does it do it? Research to date has implicated the rotational dynamics of limb movements as the major constraint on both of these questions, and this is pursued in the proposed research. Formally, the achievements of dynamic touch are related to the inertia tensor (which quantifies an object's resistance to being rotated) and the attitude spinor (which quantifies an object's orientation relative to some reference frame such as the hand). In some of the basic methodologies, participants wield an unseen object (whose structure has been specially contrived to produce the experimentally relevant inertia tensor or attitude spinor) to perceive its length, width, shape, weight, or orientation to the hand. In other basic methodologies, the participants attempt to orient a nonvisible upper limb or limb segment (with attached splints that systematically control the limb's inertia tensor and attitude spinor) to an environmental target or to another nonvisible limb. A major thesis is that, in perception by dynamic touch, the hand-related haptic subsystem behaves as a smart instrument: It capitalizes on physical, law-based, invariants. Experiments are designed to examine the consequences of different attentional demands (and the extent to which different properties are perceptually independent), different force structures (such as those experienced underwater and in rotating space stations), and in different neural conditions (such as the spurious receptor states produced when the tendons are vibrated electromagnetically). Understanding the principles governing dynamic touch should enrich the physical constraints on computational and neural modeling of perceptual systems and provide a source of new hypotheses about somatosensory disorders and about designs for prosthetic and robot limbs. Such understanding might also be expected to motivate more intensive study of the physical principles formative of biological perception-action systems and of the cognitive and neural constraints that exploit them. s partly supported by the NSF Major Research Instrumentation Program.