Dexterous robotic manipulation requires perception that remains informative from pre-contact approach to contact initiation and post-contact control. We introduce FingerEye, a sensing and learning framework that strengthens robotic dexterity through continuous vision-tactile feedback throughout interaction. On the sensing side, FingerEye integrates binocular RGB cameras with a compliant contact interface to support perception both before and after contact. Before contact, the fingertip cameras provide close-range visual cues and implicit stereo for precise approach and object localization. After contact, marker-tracked deformation of the compliant ring provides a proxy for contact wrench sensing. On the learning side, we build real-and-sim infrastructure for data collection and evaluation, systematically study policy-interface designs for learning with multiple FingerEye sensors, and develop FingerEye Policy, which applies group-structured modality fusion to reduce modality shortcuts and better exploit distributed fingertip feedback. Across seven contact-sensitive task settings, FingerEye improves wrist-only policy by over 30 percentage points in mean success rate in both simulation and the real world.