Understanding contact mechanics and adhesion processes in thin films and micro-structured materials is fundamental in phonon and heat transport phenomena and is ubiquitous for the miniaturization of mechanical and thermal devices as well as the design/functionalization of structured surfaces and membranes. Acoustic-based methods are of great interest in this context since they provide a nondestructive mean to probe interface quality and adhesion, at various scales. In particular, Laser Ultrasonics (LU) techniques allow the generation of broadband acoustic pulses with a frequency content extending up to a few THz due to the thermoelastic expansion induced by the absorption of short laser pulses. In this review, we will explore the specificities of the LU generation/detection schemes and the unusual wide frequency range that make these opto-acoustic techniques a unique tool to study adhesion processes from micro- to nanoscales, and in a variety of systems, ranging from continuous films and coatings to nano-objects. Because the size of the contact area with respect to the acoustic wavelength dictates the acoustic dispersion, we will describe separately continuous structures, in which the contact is large, before discussing micro- and nanostructured media, where the contact is localized.