Coherent phonons can be launched in materials upon localized pulsed optical excitation, and be subsequently followed in time-domain, with a sub-picosecond resolution, using a time-delayed pulsed probe. This technique yields characterization of mechanical, optical, and electronic properties at the nanoscale, and is taken advantage of for investigations in material science, physics, chemistry, and biology. Here we review the use of this experimental method applied to the emerging field of homo- and heterostructures of van der Waals materials. Their unique structure corresponding to non-covalently stacked atomically thin layers allows for the study of original structural configurations, down to one-atom-thin films free of interface defect. The generation and relaxation of coherent optical phonons, as well as propagative and resonant breathing acoustic phonons, are comprehensively discussed. This approach opens new avenues for the in situ characterization of these novel materials, the observation and modulation of exotic phenomena, and advances in the field of acoustics microscopy.