The periodic table of Mendeleev, initially proposed on the basis of 66 elements, and containing 82 elements at the time of Moseley (1887–1915), describes nowadays 118 elements. The huge challenge of this scientific adventure was, and still is, the development of technologies and methods capable of producing elements of atomic number Z > 103, known as superheavy elements (SHE), or transactinides. This paper presents a survey of experiments and theoretical approaches that led physicists and chemists of today to discover and characterize a number of SHE isotopes. A glance is also given to the feasibility studies performed by scientists aiming to going beyond Z = 118, building up further neutron-rich nuclides and reaching the ultimate goal of creating long-living new elements at the edge of the Periodic Table.