The pioneering work of Mike Batzle and his colleagues has provided a fundamental understanding of mechanisms behind dispersion and attenuation of elastic waves in fluid-saturated rocks. It also has made way for a realization that these phenomena need to be accounted for in a better way when interpreting seismic and sonic data from the field. Laboratory experiments have formed the basis for new insight in the past and will continue to do so. Here, examples of experimental observations that give direct or indirect evidence for dispersion in sand, sandstone, and shale are presented. Ultrasonic data from compaction tests show that Biot flow is the most likely dispersion mechanism in pure unconsolidated sand. Strong shale dispersion has been identified through low-frequency and low-strain quasistatic measurements and through a novel technique based on static loading and unloading measurements. In shale and sandstone containing clay, there is evidence for water weakening. A comparative study shows an example where the stress dependences of P- and S-wave velocities at seismic frequencies exceed those measured by traditional ultrasonic methods.