  We provide a phenomenological analysis of present experimental searches for
local parity violation manifested through the Chiral Magnetic Effect. We
introduce and discuss the relevant correlation functions used for the
measurements. Our analysis of the available data from both RHIC and LHC shows
that the present experimental evidence for the Chiral Magnetic Effect is rather
ambiguous. We further discuss in some detail various background contributions
due to conventional physics, which need to be understood quantitatively in
order to draw a definitive conclusion about the existence of local parity
violation in heavy ion collisions.
