Studying the properties of the few compact massive galaxies that exist in the local Universe (Trujillo et al. 2009) might provide a closer look to the nature of their high redshift (z >= 1.0) massive counterparts. By this means we have characterized their main kinematics, structural properties, stellar populations and star formation histories with a set of new high quality spectroscopic and imaging data (Ferré-Mateu et al. 2012 and Trujillo et al. 2012). These galaxies seem to be truly unique, as they do not follow the characteristic kinematics, stellar surface mass density profiles and stellar population patterns of present-day massive ellipticals or spirals of similar mass. They are, instead, more alike their high-z analogs. Summarizing, local compact massive galaxies are rare, unique and the perfect laboratory to study their high redshift counterparts.