The IceCube Neutrino Observatory, deployed beneath the South Pole, is the largest optical neutrino telescope in the World. IceCube has been measuring a diffuse flux of high-energy (TeV and above) astrophysical neutrinos for almost a decade. The sources of the vast majority of these neutrinos remain elusive, but studies indicate that gamma-ray obscured sources may at least in parts be responsible. Most recently, IceCube reported strong evidence for TeV neutrino emission from NGC 1068, a well-known and nearby active galaxy. I will explain how IceCube searches for neutrinos from astrophysical sources and how recent improvements in our analysis methods enabled this result. When put into the multi-messenger context, in particular the non-detection of TeV gamma-rays by the MAGIC telescopes, this measurement suggests that the gamma-ray obscured vicinity of the central supermassive black hole acts as a cosmic hadron accelerator. The next steps are clear. By studying similar objects we may finally identify a class of sources that makes a sizeable contribution to the diffuse flux of astrophysical neutrinos.