Some open questions for microscopic nuclear structure models and hints for spectroscopic measurements

This contribution aims at updating the non-expert reader about the successes and the drawbacks of nuclear structure models which describe the ground-state properties. The main emphasis is on models based on Density Functional Theory (DFT), with a personal bias towards the nonrelativistic implementations. After a survey about ground-state masses and a short discussion on nuclear radii, it is argued that one of the most relevant open problems is the description of single-particle states and more generally of detailed spectroscopic properties. Overall (i. e., bulk) properties are easier to reproduce and thus, less capable to discriminate between competing theories. Accordingly, it is concluded that trap-assisted detailed spectroscopic measurements are the most useful in order to improve our understanding of nuclei.