Model-based object recognition has mostly been studied over inputs including images and range data. Though such data are global, cameras and range sensors are subject to occlusions and clutters, which often make recognition difficult and computationally expensive. In contrast, touch by a robot hand is free of occlusion and clutter issues, and recognition over tactile data can be more efficient.;In this thesis, we investigate model-based recognition of two and three dimensional curved objects from tactile data. The recognition of 2D objects is an invariant-based approach. We have derived differential and semi-differential invariants for quadratic curves and special cubic curves that are found in applications. These invariants, independent of translation and rotation, can be computed from local geometry of a curve. Invariants for quadratic curves are the functions in terms of the curvature and its derivative with respect to arc length. For cubic curves, the derived invariants also involve a slope in their expressions. Recognition of a curve reduces to invariant verification with its canonical parametric form determined along the way. In addition, the contact locations with the robot hand are found on the curve, thereby localizing it relative to the touch sensor. We have verified the correctness of all invariants by simulations. We have also shown that the shape parameters of the recognized curve can be recovered with small errors. The byproduct is a procedure that reliably estimates curvature and its derivative from real tactile data. The presented work distinguishes itself from traditional model-based recognition in its ability to simultaneously recognize and localize a shape from one of several classes, each consisting of a continuum of shapes, by the use of local data.;The recognition of 3D objects is based on registration and consists of two steps. First, a robotic hand with touch sensors samples data points on the object's surface along three concurrent curves. The two principal curvatures at the curve intersection point are estimated and then used in a table lookup to find surface points that have similar local geometries. Next, starting at each such point, a local search is conducted to superpose the tactile data onto the surface model. Recognition of the model is based on the quality of this registration. The presented method can recognize algebraic as well as free-form surfaces, as demonstrated via simulations and robot experiments. One difference in the recognition of these two sets of shapes lies in the principal curvature estimation, which are calculated from the close forms and estimated through fitting, respectively. The other difference lies in data registration, which is carried out by nonlinear optimization and a greedy algorithm, respectively.