This thesis introduces the concept of TEXterity (Tactile Extrinsic deXterity) to address challenges in robotic manipulation. Focusing on tactile sensing, TEXterity aims to enhance dexterity by enabling robots to perceive and act upon extrinsic contact between the grasped object and the environment. Identifying interpretability, observability, and uncertainty as key challenges in tactile sensing, this thesis sets out to answer four pivotal questions:

1. Is tactile sensing actually useful?
2. How can we exploit tactile sensing efficiently?
3. How can we reason about extrinsic contact with tactile sensing?
4. How can we achieve extrinsic dexterity with tactile sensing?

The conclusion summarizes the key findings, emphasizing the significance of tactile sensing and TEXterity in addressing challenges and advancing robotic manipulation. Strategies to tackle major challenges are outlined, focusing on interpretability, observability, and uncertainty. In essence, this thesis lays the groundwork for unlocking the potential of tactile sensing in robotic manipulation, offering insights, solutions, and avenues for future research to propel the field toward achieving TEXterity and further toward human-level dexterity.