Abstract: The exploration of the limit to the existence of nuclides in terms of proton and mass numbers, naturally related to the synthesis of new chemical elements, is a foremost subject of nuclear physics. The synthesis of new elements and exploration of the stability island of superheavy nuclides predicted a long time ago have stimulated extensive research both experimentally and theoretically. The overarching important topics include: How many chemical elements can exist? What are the chemical properties of superheavy elements? Up to which element is the ordering scheme of Mendeleev's periodic table still valid? What are the maximum proton and neutron magic numbers? Are there stable or long-lived superheavy nuclides? What exotic structures and properties of superheavy nuclides appear under extremely strong Coulomb fields? And so forth. Over the last half century, momentous achievements in the synthesis of transuranium nuclides and elements have been made. To date, superheavy elements with atomic number up to 118 and hundreds of superheavy nuclides have been discovered in various laboratories, resulting in the completion of the seventh period of the periodic table of elements. This paper reviews the search for superheavy elements in nature and the artificial synthesis of transuranium nuclides and elements using nuclear reactions induced by high neutron flux and energic heavy ions, and presents a perspective on the field of superheavy nuclide studies, with an emphasis on the High Intensity Heavy-ion Accelerator Facility of the Major National Science and Technology Infrastructure Facilities Program in China.