I believe robot dexterity is not only about the robot's physical flexibility (characterized by more joints), but instead, we should consider it as a critical form of artificial intelligence. This talk presents some of my thoughts about opportunities we could open up about robot dexterity. My past work discusses a question, " Where could a robot discover more dexterity?". I will present the idea that we could expand the frontier of robot dexterity by using all elements present in the task environments: not only the robot fingertips but also the environment and other existing features of the robot. For example, a robot can find dexterity in even the simplest gripper, a suction cup designed solely for pick-and-place. By fully considering the suction cup soft bellow and exploiting the environment contacts, the robot can reorient an object, even in a way that a rigid robot finger cannot do. Second, the surrounding environment is an effective tool to enhance dexterity. I will present my series of works that generate various dexterous manipulation strategies by considering the present environment, without using any manually engineered primitives. Finally, I hope to discuss with you broadly about new opportunities for dexterity I discovered in this journey.