Future electronic skin aims to mimic nature's original both in functionality and appearance. Although some of the multifaceted properties of human skin may remain exclusive to the biological system, electronics opens a unique path that leads beyond imitation and could equip us with unfamiliar senses. Here we demonstrate giant magnetoresistive sensor foils with high sensitivity, unmatched flexibility and mechanical endurance. They are <2 μm thick, extremely flexible (bending radii <3 μm), lightweight (≈3 g m(-2)) and wearable as imperceptible magneto-sensitive skin that enables proximity detection, navigation and touchless control. On elastomeric supports, they can be stretched uniaxially or biaxially, reaching strains of >270% and endure over 1,000 cycles without fatigue. These ultrathin magnetic field sensors readily conform to ubiquitous objects including human skin and offer a new sense for soft robotics, safety and healthcare monitoring, consumer electronics and electronic skin devices.