Robotic manipulation of everyday objects and dependable execution of household chores is one of the most desired and challenging skills for future service robots. Most of the current research in robotic grasping is limited to pick-and-place tasks, without paying attention to the whole range of different tasks needed in human environments, such as opening doors, interacting with furniture, household electrical appliances , etc. In this article, a sensor-based integrated framework for specifying both the grasp and the task is presented, with the goal of motivating dependable task-oriented grasping and manipulation. The grasp is defined as a desired task-suitable relationship between the robot hand and the object being manipulated. The task is defined under the task frame formalism [1], which allows to specify tasks for sensor-guided dependable interaction. Some guidelines for sensor-based execution of tasks defined under the proposed formalism are also given. Three different examples of dependable manipulation tasks, performed by three different robots, are presented, making use of the proposed approach and disparate sensor information: book grasping by tactile-force integration, door opening by vision-force control, and force-guided humanoid interaction with kitchen furniture.