This paper provides a systematic classification of the different measures of polarization based on their properties. Together with the axioms proposed in Duclos, Esteban and Ray (2004) and in Wang and Tsui (2000) we consider three additional properties. We examine which properties are common to all indices and which set them apart.Financial support from the Instituto de Estudios Fiscales and the CICYT (SEC-2003-1961) is gratefully acknowledged. This research is part of the Polarization and Conflict research project CIT2-CT-2004-506084 funded by the European Commission-DG Research Sixth Framework Programme