The structure of very heavy and superheavy nuclei (SHN) as well as the location of the next proton and neutron shell closures beyond 208Pb is still one of the most intriguing topics in modern nuclear physics [1]. Worldwide competitive, high beam intensities provided by the accelerator facility SPIRAL2 at GANIL which started operation recently, will cover in future all ions up to uranium thanks to the new injector project NEWGAIN. Combined with the separator-spectrometer installation S3 [3], it will provide the instrumental prerequisites for an ambitious science program. Apart from SHN/SHE research, the envisaged physics case at S3 covers, among other, the structure of N=Z nuclei, low energy physics (fundamental properties of the atomic nucleus etc.), interdisciplinary research, atomic physics and reaction studies (fission, deep inelastic reactions etc.). The state of the art of the field is discussed in this paper with an emphasis on the role of the odd particle(s) in odd-even, even-odd and odd-odd nuclei and the consequences for nuclear structure features like K-isomers, trends of single-particle energies as a function of deformation, and the competition of spontaneous fission (SF) and α decay. As an alternative approach to produce heavy and in particular more neutron-rich nuclear species multi-nucleon transfer reactions are briefly discussed as well.