Neutrinos remain mysterious: do they have sizable self-interactions? Laboratory probes allow enhanced self-interactions (also known as secret interactions or νSI). These can be more than 10 orders of magnitude stronger than weak interactions, and they have been invoked to explain several anomalies or dark matter production. νSI are also key to interpret cosmology data, where hints for them exist. In this talk, I will overview the phenomenology of νSI, and discuss how astrophysical neutrino observations provide key sensitivity. I will review how νSI distort the spectra of high-energy astrophysical neutrinos, and how next-generation probes will be uniquely sensitive.  I will also discuss observables from core-collapse supernovae, where we might be close to solving a 30-year-old puzzle and, at the same time, increasing sensitivity to νSI by about 4 orders of magnitude. Altogether, I will argue that astroparticle physics observables will be essential to test a fundamental neutrino property — the existence of self-interactions — with major consequences in other areas of physics and astrophysics.