We discuss some of the interesting physics behind the design and operation of the Theremin electronic musical instrument. To complement the theory we present details of a parallel effort to construct two versions of this remarkable instrument. One of these designs remains fairly faithful to the traditional beat frequency oscillator approach that first inspired Theremin's invention, while the other contains more modern electronics that helps make more reliable the setting up and use of the instrument. The emphasis on the physical principles continues into a comparison of the two instruments. Following completion, the Theremins have been extensively used in public and schools science exhibitions and in lecture demonstrations.