We introduce MoiréWidgets, a novel approach for tangible interaction that harnesses the Moiré effect—a prevalent optical phenomenon—to enable high-precision event detection on physical widgets. Unlike other electronics-free tangible user interfaces which require close coupling with external hardware, MoiréWidgets can be used at greater distances while maintaining high-resolution sensing of interactions. We define a set of interaction primitives, e.g., buttons, sliders, and dials, which can be used as standalone objects or combined to build complex physical controls. These consist of 3D printed structural mechanisms with patterns printed on two layers—one on paper and the other on a plastic transparency sheet—which create a visual signal that amplifies subtle movements, enabling the detection of user inputs. Our technical evaluation shows that our method outperforms standard fiducial markers and maintains sub-millimeter accuracy at 100 cm distance and wide viewing angles. We demonstrate our approach by creating an audio console and indicate how our approach could extend to other domains.