For almost three decades it has been known that the study of astrophysically important nuclear reactions between stable nuclei requires the use of low-background, underground accelerator laboratories. The Felsenkeller shallow-underground laboratory in Dresden, shielded by a 45 m thick rock cover, hosts a 5 MV Pelletron ion accelerator with an external sputter ion source (mainly able to provide carbon and oxygen beams) and an internal radio-frequency ion source (providing proton and alpha beams). The reduced muon, neutron and gamma-ray background achieved both with natural and active shielding situate the laboratory well in line with deep underground accelerator labs worldwide and allows highly sensitive nuclear reaction experiments. Currently, measurements affecting the solar fusion and Big Bang nucleosynthesis are ongoing. In addition to in-house research by HZDR and TU Dresden, the lab is an open facility for scientific users worldwide, with beam time applications reviewed by an independent science advisory board. Furthermore, EU-supported transnational access is available via the ChETEC- INFRA network for nuclear astrophysics. A brief introduction to underground nuclear astrophysics, status of the Felsenkeller shallow-underground laboratory and some preliminary results are discussed.