The human hand is an amazing tool, demonstrated by its incredible motor capability and remarkable sense of touch. To enable robots to work in a human-centric environment, it is desirable to endow robotic hands with human-like capabilities for grasping and object manipulation. However, due to its inherent complexity and inevitable model uncertainty, robotic grasping and manipulation remains a challenge. This thesis focuses on grasp adaptation in the face of model and sensing uncertainties: Given an object whose properties are not known with certainty (e.g., shape, weight and external perturbation), and a multifingered robotic hand, we aim at determining where to put the fingers and how the fingers should adaptively interact with the object using tactile sensing, in order to achieve either a stable grasp or a desired dynamic behaviour. A central idea in this thesis is the object-centric dynamics: namely, that we express all control constraints into an object-centric representation. This simplifies computa- tion and makes the control versatile to the type of hands. This is an essential feature that distinguishes our work from other robust grasping work in the literature, where generating a static stable grasp for a given hand is usually the primary goal. In this thesis, grasp adaptation is a dynamic process that flexibly adapts the grasp to fit some purpose from the objectâ s perspective, in the presence of a variety of uncertainties and/or perturbations. When building a grasp adaptation for a given situation, there are two key problems that must be addressed: 1) the problem of choosing an initial grasp that is suitable for future adaptation, and more importantly 2) the problem of design- ing an adaptation strategy that can react adequately to achieve desired behaviour of the grasped object. To address challenge 1 (planning a grasp under shape uncertainty), we propose an approach to parameterizing the uncertainty in object shape using Gaussian Processes (GPs) and incorporate it as a constraint into contact-level grasp planning. To realize the planned contacts using different hands interchangeably, we further develop a prob- abilistic model to predict the feasible hand configurations, including hand pose and finger joints, given the desired contact points only. The model is built using the con- cept of Virtual Frame(VF), and it is independent from the choice of hand frame and object frame. The performance of the proposed approach is validated on two differ- ent robotic hands, an industrial gripper (4 DOF Barrett hand) and a humanoid hand (16 DOF Allegro hand) to manipulate objects of daily use with complex geometry and various texture (a spray bottle, a tea caddy, a jug and a bunny toy). In the second part of this thesis, we propose an approach to the design of adapta- tion strategy to ensure grasp stability in the presence of physical uncertainties of objects(object weight, friction at contacts and external perturbation). Based on an object-level impedance controller, we first design a grasp stability estimator in the object frame using the grasp experience and tactile sensing. Once a grasp is predicted to be unstable during online execution, the grasp adaptation strategy is triggered to improve the grasp stability, by either changing the stiffness at finger level or relocating the position of one fingertip to a better area.