Abstract The use of mechanical resonances to test properties of materials is older than the industrial revolution. Early documented cases of British railroad engineers tapping the wheels of a train and using the sound to detect cracks perhaps marks the first real use of resonances to test the integrity of high-performance alloys. Attempts were made in the following years to understand the resonances of solids mathematically, based on shape and composition. But Nobel Laureate Lord Rayleigh best summarized the state of affairs in 1894, stating ‘the problem has, for the most part, resisted attack’. More recently, modern computers and electronics have enabled Anderson and co-workers, with their work on minerals, and our work at Los Alamos on new materials and manufactured components, to advance the use of resonances to a precision non-destructive testing tool that makes anisotropic modulus measurements, defect detection and geometry error detection routine. The result is that resonances can achieve the highest absolute accuracy for any routine dynamic modulus measurement technique, can be used on the smallest samples, and can also enable detection of errors in certain classes of precision manufactured components faster and more accurately than any other technique.