Nuclear reactions leading to the formation of new superheavy (SH) elements and isotopes are discussed in the paper. “Cold” and “hot” synthesis, fusion of fission fragments, transfer reactions, and reactions with radioactive ion beams are analyzed along with their abilities and limitations. If the possibility of increasing the beam intensity and the detection efficiency (by a total of one order of magnitude) is found, then several isotopes of new elements with Z=120-124 could be synthesized in fusion reactions of titanium, chromium, and iron beams with actinide targets. The use of light- and medium-mass neutron-rich radioactive beams may help us fill the gap between the SH nuclei produced in the hot fusion reactions and the mainland. In these reactions, we may really approach the “island of stability.” Such a possibility is also provided by the multinucleon transfer processes in low-energy damped collisions of heavy actinide nuclei. The production of SH elements in fusion reactions with accelerated fission fragments looks less encouraging.