  We review the progress in atomic structure theory with a focus on superheavy
elements and the aim to predict their ground state configuration and element's
placement in the periodic table. To understand the electronic structure and
correlations in the regime of large atomic numbers, it is important to
correctly solve the Dirac equation in strong Coulomb fields, and also to take
into account quantum electrodynamic effects. We specifically focus on the
fundamental difficulties encountered when dealing with the many-particle Dirac
equation. We further discuss the possibility for future many-electron atomic
structure calculations going beyond the critical nuclear charge \(Z_{\rm
crit}\approx 170\), where levels such as the \(1s\) shell dive into the
negative energy continuum (\(E_{n\kappa}<-m_ec^2\)). The nature of the
resulting Gamow states within a rigged Hilbert space formalism is highlighted.
