Selected issues at the interface between nuclear physics and astrophysics as well as the standard model

The density functional theory (DFT) with a minimal number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. The recent developments on the application of the covariant density functional theory as well as its extensions by the group in Beijing for a series of interests and hot topics in nuclear astrophysics and nuclear structure are reviewed, including the rapid neutron-capture process, Th/U chronometer, and isospin corrections for superallowed β transitions.