Rapidly developing neutrino physics has found in Penning-trap mass spectrometry a staunch ally in investigating and contributing to a variety of fundamental problems. The most familiar are the absolute neutrino mass and the possible existence of resonant neutrinoless double-electron capture / double-beta dacay and of keV-sterile neutrinos. This review provides an overview on the latest achievements and future perspectives of Penning-trap mass spectrometry on short-lived as well as stable nuclides with applications in nuclear structure, neutrino physics and most recently even in dark matter searches where relative mass uncertainties at the level of 10-11 and below are required.