We characterize the kinematics , morphology , stellar populations and star formation histories of a sample of massive compact galaxies in the nearby Universe , which might provide a closer look to the nature of their high redshift ( z \ga 1.0 ) massive counterparts . We find that nearby compact massive objects show elongated morphologies and are fast rotators . New high-quality long-slit spectra show that they have young mean luminosity-weighted ages ( \la 2 Gyr ) and solar metallicities or above ( [ Z/H ] \ga 0.0 ) . No significant stellar population gradients are found . The analysis of their star formation histories suggests that these objects have experienced recently enormous bursts which , in some cases , represent unprecedented large fractions of their total stellar mass . These galaxies seem to be truly unique , as they do not follow the characteristic kinematical and stellar population patterns of present-day massive ellipticals , spirals or even dwarfs .