Structure-property relationships are the foundation of materials science.Linking microstructure and material properties is essential for predicting material response to driving forces, managing in-service material degradation, and engineering materials for optimal performance. Elastic, thermal, and acoustic properties provide a convenient gateway to directly or indirectly probe material structure across multiple length scales. We review how using the laser-induced transient grating spectroscopy (TGS) technique, which uses a transient diffraction grating to generate surface acoustic waves (SAWs) and temperature gratings on a material surface, non-destructively reveals the material's elasticity, thermal diffusivity, and energy dissipation on the sub-microsecond timescale, within a tunable sub-surface depth. This technique has already been applied to many challenging problems in materials characterization, from analysis of radiation damage, to colloidal crystals, to phonon-mediated thermal transport in nanostructured systems, to crystal orientation and lattice parameter determination.Examples of these applications, as well as inferring aspects of microstructural evolution, illustrate the wide potential reach of TGS to solve old materials challenges, and to uncover new science. We conclude by looking ahead at the tremendous potential of TGS for materials discovery and optimization when applied in situ to dynamically evolving systems.