The heaviest nuclei have been investigated near the limits of stability in charge, spin and excitation energy. They have so many protons that their Coulomb repulsion should cause spontaneous fission. Yet elements with atomic weight up to 118 appear to exist, based on recent reports from Dubna. The heaviest nuclei survive because a quantal effect, the shell-correction energy, gives extra binding, which creates a barrier against fission. The stabilization is largest when protons and neutrons fill shells up to a "magic" energy gap, analogous to inert gases with filled electron shells in atoms. In the quest for nuclei with the largest number of protons, the view of the "island of stability", a predicted region of superheavy nuclei in the nuclear chart, is now becoming clear. Excited states have been found in 254No, a nucleus with the largest number of protons (102) studied using spectroscopy. The energies of these states provide critical tests of theories of superheavy nuclei and, thereby, discriminate among their predictions of the center of the island of stability. The best candidate for the center, where there is a "magic" energy gap, is at proton number 114. This result supports a long-standing prediction and challenges conflicting suggestions of modern self-consistent mean-field theories. Loosely bound nuclei such as nobelium are expected to be fragile, yet experiments at Argonne have shown them to be surprisingly robust. The resilient survival of superheavy nuclei with atomic weight up to perhaps Z=118, well past the onset of spontaneous fission in uranium (Z=92), is an interesting phenomenon in nuclear physics.

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