We begin by identifying the fascinating behavior of most of the thin, flexible magnets normally described as “refrigerator magnets.” Simple procedures are described that illustrate the intriguing physics of these magnets, which produce fields characterized by spatial variations that are quite abrupt compared to those of the more common ceramic magnets. A method is suggested for producing profiles of this spatial variation. The method is based on the use of magnetic field sensors that employ a novel phenomenon called giant magnetoresistance. After reviewing GMR and the sensors, we describe our field-mapping procedure and discuss the results.