The chiral magnetic effect (CME) in quantum chromodynamics (QCD) refers to a charge separation (an electric current) of chirality imbalanced quarks generated along an external strong magnetic field. The chirality imbalance results from interactions of quarks, under the approximate chiral symmetry restoration, with metastable local domains of gluon fields of non-zero topological charges out of QCD vacuum fluctuations. Those local domains violate the P and CP invariance, potentially offering a solution to the strong CP problem in explaining the magnitude of the matterantimatter asymmetry in today's universe. Relativistic heavy-ion collisions, with the likely creation of the high energy density quark-gluon plasma and restoration of the approximate chiral symmetry, and the possibly long-lived strong magnetic field, provide a unique opportunity to detect the CME. Early measurements of the CME-induced charge separation in heavy-ion collisions are dominated by physics backgrounds. Major efforts have been devoted to eliminate or reduce those backgrounds. We review those efforts, with a somewhat historical perspective, and focus on the recent innovative experimental undertakings in the search for the CME in heavy-ion collisions.Keywords: heavy-ion collisions, chiral magnetic effect, three-point correlator, elliptic flow background, invariant mass, harmonic plane Our universe started from the Big Bang singularity [1] with equal amounts of matter and antimatter, but is today dominated by only matter. No significant concentration of antimatter has ever been found in the observable universe [2]. This matter-antimatter asymmetry is caused by CP (chargeconjugation parity) violation, a slight difference in the physics governing matter and antimatter [3,4], as in e.g. electroweak baryogenesis [5,6]. CP is violated in the weak interaction but the magnitude of the CKM quark-sector CP violation [7,8] is too small to explain the present universe matter-antimatter asymmetry [9]. It is unclear whether the lepton-sector CP violation through leptogenesis [3,10] is large enough to account for the matter-antimatter asymmetry. CP violation in the strong interaction in the early universe may be needed. CP violation is not prohibited in the strong interaction [11] but none has been experimentally observed [12,13]. This is called the strong CP problem [11,14]. To solve the strong CP problem, Peccei and Quinn [14,15] proposed to extend the QCD (quantum chromodynamics) Lagrangian by a CP-violating θ term, first introduced by 't Hooft [16,17] in resolving the axial U (1) problem [18]. It predicts the existence of a new particle called the axion. If axions exist, they would not only offer a solution to the strong CP problem, but could also be a dark matter candidate [19]. On the other hand, the Peccei-Quinn mechanism would remove the large, flavour diagonal CP violation, precluding a solution to the strong CP problem to arise from QCD. However, axions have not been detected after four decades of search since its conception [20,21].Here, we concent...