We discuss recent results in neutrino astronomy and their implications for the cosmic-ray acceleration in relativistic outflows, such as in Active Galactic Nuclei (AGN) jets, Gamma-Ray Bursts (GRBs), and Tidal Disruption Events (TDEs). We especially focus on challenges at the interface to particle acceleration which can be inferred from the multi-messenger context, such as the paradigm that the sources power the Ultra-High-Energy Cosmic Rays (UHECRs). We demonstrate that both AGN blazars (in the context of neutrino observations) and GRBs (as UHECR sources in the context of neutrino-non-observations) point towards acceleration spectra harder than E^-2, or relatively high minimal cosmic-ray injection energies, to meet the respective energy budget requirements. We furthermore speculate that neutrino flares in blazars may be related to super-Eddington accretion flares, or that GRBs are powered by significantly higher kinetic energies than typically assumed in electromagnetic models. For internal shock models, the UHECR paradigm for GRBs can only be maintained in the light of neutrino stacking limits in multi-zone models. While relativistic outflows in TDEs have become recently interesting per se and models for the neutrino emission from jetted TDEs exist, a direct connection between TDE jets pointing in our direction and astrophysical neutrinos has not been identified yet.