Recent progress on hydrogen and helium burning at the LUNA 400 kV underground accelerator

n-beam radiative-capture experiments at low astrophysical energies require experiments in ultra-low background conditions. The Laboratory for Underground Nuclear Astrophysics (LUNA) 0.4\,MV accelerator at INFN Gran Sasso, Italy, is so far the only underground ion accelerator in the world. Recent progress at LUNA regarding the $^{22}$Ne(p,$\gamma$)$^{23}$Na [1,2], $^{22}$Ne($\alpha$,$\gamma$)$^{26}$Mg, and $^{17}$O(p,$\alpha$)$^{14}$N [3] reactions will be reviewed. The project for the new, 3.5 MV LUNA-MV accelerator is on track and will be summarized.