The Zwicky Transient Facility (ZTF) performs a systematic neutrino follow-up program, searching for optical counterparts to high-energy neutrinos. Since first light in March 2018, ZTF has taken prompt observations for 24 high-quality neutrino alerts from the IceCube Neutrino Observatory. What optical follow-up has taught us about neutrino sources? From two of these campaigns, we identified tidal disruption event (TDE) AT2019dsg and likely TDE AT2019fdr as probable counterparts. Using the non-detections from other campaigns, we also place the first constraints on the underlying optical luminosity function of astrophysical neutrino sources. These are the first observational constraints on the neutrino emission of bright populations such as superluminous supernovae. I will also highlight the future outlook for neutrino follow-up, especially the imminent start of an infra-red follow-up program with the Wide-Field Infrared Transient Explorer (WINTER).