ABSTRACT We present optical follow-up observations with the Deca-Degree Optical Transient Imager (DDOTI) telescope of gravitational-wave (GW) events detected during the Advanced LIGO and Advanced Virgo O3 observing run. DDOTI is capable of responding to an alert in a few minutes, has an instantaneous field of about 69 deg2, and obtains 10σ upper limits of wlim = 18.5–20.5 AB mag in 1000 s of exposure, depending on the conditions. We observed 54 per cent (26 out of 48) of the unretracted GW alerts and did not find any electromagnetic counterparts. We compare our upper limits to various possible counterparts: the kilonova AT 2017gfo, models of radioactive- and magnetar-powered kilonovae, short gamma-ray burst afterglows, and active galactic nucleus (AGN) flares. Although the large positional uncertainties of GW sources do not allow us to place strong constraints during O3, DDOTI observations of well-localized GW events in O4 and beyond could meaningfully constrain models of compact binary mergers. We show that DDOTI is able to detect kilonovae similar to AT 2017gfo up to about 200 Mpc and magnetar-powered kilonovae up to 1 Gpc. We calculate that nearby (≲200 Mpc) afterglows have a high chance (≈70 per cent) to be detected by rapid (≲3 h) DDOTI observations if observed on-axis, whereas off-axis afterglows are unlikely to be seen. Finally, we suggest that long-term monitoring of massive BBH events with DDOTI could confirm or rule out late AGN flares associated with these events.