ABSTRACT We report on the search for optical counterparts to IceCube neutrino alerts released between 2016 April and 2021 August with the All-Sky Automated Survey for SuperNovae (ASAS-SN). Despite the discovery of a diffuse astrophysical high-energy neutrino flux in 2013, the source of those neutrinos remains largely unknown. Since 2016, IceCube has published likely astrophysical neutrinos as public real-time alerts. Through a combination of normal survey and triggered target-of-opportunity observations, ASAS-SN obtained images within 1 h of the neutrino detection for 20 per cent (11) of all observable IceCube alerts and within one day for another 57 per cent (32). For all observable alerts, we obtained images within at least two weeks from the neutrino alert. ASAS-SN provides the only optical follow-up for about 17 per cent of IceCube’s neutrino alerts. We recover the two previously claimed counterparts to neutrino alerts, the flaring-blazar TXS 0506 + 056 and the tidal disruption event AT2019dsg. We investigate the light curves of previously detected transients in the alert footprints, but do not identify any further candidate neutrino sources. We also analysed the optical light curves of Fermi 4FGL sources coincident with high-energy neutrino alerts, but do not identify any contemporaneous flaring activity. Finally, we derive constraints on the luminosity functions of neutrino sources for a range of assumed evolution models.