The review considers physics and some applications of a new approach that promises to be a breakthrough in efficiency and instrumentation of various methods for nondestructive testing (NDT) of composites. The approach is based on frequency-selective properties of defects which fall into resonance (Local Defect Resonance (LDR)) at certain frequencies. An activation of LDR enables to route the input acoustic energy directly to the defect that dramatically increases its vibration amplitude and thus facilitates defect-selective imaging, rises efficiencies of various derivative acoustic NDT methods (nonlinear, acousto-thermal) and enables to develop some new methodologies, like Resonant Air-Coupled Emission (RACE), machine and remote imaging.