The physics of nuclear collective motion was pioneered by A Bohr and B R Mottelson 50 years ago. Since then, experimental and theoretical development in this field has been remarkable under the leadership of the Copenhagen group. In the 21st century, a new era has opened up due to the recent developments of experimental facilities, especially radioactive ion beams and large γ-ray arrays. Interest in collective motions is now shared in the research of other quantum many-body systems — for example, microclusters and Bose-Einstein condensation. It is therefore timely and important...