In this paper, we review results obtained by ultrafast imaging of gigahertz surface acoustic waves in surface phononic crystals with one-and two-dimensional periodicities. By use of quasi-point-source optical excitation, we show how, from a series of images that form a movie of the travelling waves, the dispersion relation of the acoustic modes, their corresponding mode patterns and the position and widths of phonon stop bands can be obtained by temporal and spatiotemporal Fourier analysis. We further demonstrate how one can follow the temporal evolution of phononic eigenstates in k-space using data from phononic-crystal waveguides as an example.