Nonlinear elastic wave spectroscopy (NEWS) represents a class of powerful tools which explore the dynamic nonlinear stress–strain features in the compliant bond system of a micro-inhomogeneous material and link them to micro-scale damage. Hysteresis and nonlinearity in the constitutive relation (at the micro-strain level) result in acoustic and ultrasonic wave distortion, which gives rise to changes in the resonance frequencies as a function of drive amplitude, generation of accompanying harmonics, nonlinear attenuation, and multiplication of waves of different frequencies. The sensitivity of nonlinear methods to the detection of damage features (cracks, flaws, etc.) is far greater than can be obtained with linear acoustical methods (measures of wavespeed and wave dissipation). We illustrate two recently developed NEWS methods, and compare the results for both techniques on roofing tiles used in building construction.