We introduce perioperation, a paradigm for robotic data collection that sensorizes and records human manipulation while maximizing the transferability of the data to real robots. We implement this paradigm in DEXOP, a passive hand exoskeleton designed to maximize human ability to collect rich sensory (vision + tactile) data for diverse dexterous manipulation tasks in natural environments. DEXOP mechanically connects human fingers to robot fingers, providing users with direct contact feedback (via proprioception) and mirrors the human hand pose to the passive robot hand to maximize the transfer of demonstrated skills to the robot. The force feedback and pose mirroring make task demonstrations more natural for humans compared to teleoperation, increasing both speed and accuracy. We evaluate DEXOP across a range of dexterous, contact-rich tasks, demonstrating its ability to collect high-quality demonstration data at scale. Policies learned with DEXOP data significantly improve task performance per unit time of data collection compared to teleoperation, making DEXOP a powerful tool for advancing robot dexterity. Our project page is at https://dex-op.github.io.