The recent progress of multiple chiral doublet bands (MχD) is reviewed for both experimental and theoretical sides. In particular, the experimental findings, theoretical predictions, selection rule for electromagnetic transitions, MχD with octupole correlations and some related topics are highlighted. Based on these discussions, it is of highly scientific interest to search for the more MχD as well as the possible chiral wobblers, chirality-parity quartet and chirality-pseudospin triplet (or quartet) bands in nuclear system.