We discuss certain mechanisms for the creation of a charge asymmetry with respect to the reaction plane among hadrons emitted in relativistic heavy-ion collisions and show that such mechanisms exist in both, the hadronic gas and the partonic phases of QCD. All such mechanisms have in common that they require the presence of a strong magnetic field (the "chiral magnetic effect"), but they do not involve parity or charge-parity violations. We analyze how a transient local electric current generated by the chiral magnetic effect can dynamically evolve into a charge asymmetry of the final-state hadron distribution in momentum space. We estimate the magnitude of the event-by-event fluctuations of the final-state charge asymmetry due to the partonic and hadronic mechanisms.