Anomalous chiral transport processes, with the notable examples of Chiral Magnetic Effect (CME) and Chiral Magnetic Wave (CMW), are remarkable phenomena that stem from highly nontrivial interplay of QCD chiral symmetry, axial anomaly, and gluonic topology. The heavy ion collisions provide a unique environment where a hot chiral-symmetric quark-gluon plasma  is created, gluonic topological fluctuations generate chirality imbalance, and very strong magnetic fields $|\vec{\bf B}|\sim m_\pi^2$ are present during the early stage of such collisions. Significant experimental efforts have been made to look for signals of CME and various other signals of anomalous chiral transport effects in heavy ion collisions. Crucial for such efforts, is the theoretical development of quantitative simulations based on hydrodynamics that incorporates chiral anomaly, implements realistic initial conditions and properly accounts for possible backgrounds. We present an overview of recent exciting experimental and theoretical progress. We also give an outlook on anticipated developments in the near future, within the context of the recently formed Beam Energy Scan Theory (BEST) Collaboration.