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Heavy-ion collisions generate extremely hot quark-gluon plasma under the influence of extremely strong electromagnetic fields and extremely fast local rotation (flow vorticity). Once coupled to chiral anomaly, the electromagnetic field and vorticity may induce novel transport phenomena if the quark-gluon plasma contains P- and CP-odd bubbles. Such anomalous chiral transports include chiral magnetic effect, chiral vortical effect, chiral magnetic waves, chiral vortical waves, etc. We discuss the underlying mechanism of these anomalous chiral transports and the current status of their experimental search in heavy-ion collisions. We will also discuss the connection to condensed matter systems.