Abstract: The study of superheavy nuclei and superheavy elements and the exploration of the existence limits of the charge and mass of atomic nuclei is at the forefront of modern science.The existence of superheavy nuclei is mainly due to quantum shell effects. In the 1960s,based on the stability originating from shell effects, it was predicted that an island of stability centered at Z=114 and N=184 should exist. This prediction advanced the construction of heavy ion accelerators and related detectors and the development of heavy ion physics. So far, new elements with a charge number up to 118 have been synthesized in laboratories. The elements with Z=116 and 114 and Z<113 have already been named. There are many challenges to synthesize even heavier elements by using heavy ion fusion reactions. More efforts should be made to study the properties of superheavy nuclei both experimentally and theoretically. In this article, the background, experimental progress, and challenges concerning the study of superheavy nuclei will be presented,and future prospects discussed.