  Relativistic heavy ion collisions represent an arena for the probe of various
anomalous transport effects. Those effects, in turn, reveal the correspondence
between the solid state physics and the high energy physics, which share the
common formalism of quantum field theory. It may be shown that for the wide
range of {field-theoretic} models, the response of various nondissipative
currents to the external gauge fields is determined by the momentum space
topological invariants. Thus, the anomalous transport appears to be related to
the investigation of momentum space topology -- the approach developed earlier
mainly in the condensed matter theory. Within this methodology we analyse
systematically the anomalous transport phenomena, which include, in particular,
the anomalous quantum Hall effect, the chiral separation effect, the chiral
magnetic effect, the chiral vortical effect and the rotational Hall effect.
