In this talk, we present the theory of asymptotic observers on the exemplary case of wave-like equations. We show how this approach allows to use heterogeneous types of data in order to reconstruct a trajectory, estimate the initial conditions or identify some parameters. We present a complete analysis and numerical analysis of the strategy. The question of the data sampling and the impact of noise is also studied. Finally, we illustrate the approaches on various practical cases, from the wave equation in bounded of unbounded domain to elastodynamics models.