In vivo assessment of dispersion affecting the propagation of visco-elastic waves in soft tissues is key to understand the rheology of human tissues. In this paper, the ability of the supersonic shear imaging (SSI) technique to generate planar shear waves propagating in tissues is fully exploited. First, by strongly limiting shear wave diffraction in the imaging plane, this imaging technique enables to discriminate between the usually concomitant influences of both medium rheological properties and diffraction affecting the shear wave dispersion. Second, transient propagation of these plane shear waves in soft tissues can be measured using echographic images acquired at very high frame. In vitro and in vivo experiments demonstrate that dispersion curves, which characterize the rheological behavior of tissues by measuring the frequency dependence of shear wave speed and attenuation, can be recovered in the 75-600 Hz frequency range. Based on a phase difference algorithm, the dispersion curves are computed in 1 cm2 regions of interest from the acquired propagation movie. In vivo measurements in Biceps Brachii muscle and liver of three healthy volunteers show important differences in the rheological behavior of these different tissues. Liver tissue appears to be much more dispersive with a phase velocity ranging from approximately 1.5 m/s at 75 Hz to approximately 3 m/s at 500 Hz whereas muscle tissue shows an important anisotropy, shear waves propagating longitudinally to the muscular fibers are almost nondispersive while those propagating transversally are very dispersive with a shear wave speed ranging from 0.5 to 2 m/s between 75 and 500 Hz. The estimation of dispersion curves is local and can be performed separately in different regions of the organ. This signal processing approach based on the SSI modality introduces the new concept of in vivo shear wave spectroscopy (SWS) that could become an additional tool for tissue characterization. This paper demonstrates the in vivo ability of this SWS to quantify both local shear elasticity and dispersion in real time.