Next-generation facilities will probe with unprecedented depth and coverage the rates of core-collapse supernovae (CCSNe) both in the local and the high-z Universe. However, rest-frame optical transient surveys miss a significant fraction of CCSNe, and observed star formation and CCSN rates show a discrepancy. From z ~ 1 onwards, luminous infrared galaxies (LIRGs; 10^11 L_Sun < L_IR < 10^12 L_Sun) dominate star formation and CCSN production; however, the bulk of this is heavily dust obscured in these galaxies. In order to discover and study CCSNe in LIRGs, and to quantify the undetectable fraction of CCSNe in these galaxies, our SUNBIRD collaboration has carried out adaptive optics assisted monitoring programmes at Gemini-N, Gemini-S, Keck, and VLT telescopes of samples of LIRGs. The programmes have resulted in discoveries of heavily obscured CCSNe and provided evidence that LIRGs favour certain CCSN subtypes based on the age of their starburst. Furthermore, we have derived missing fraction and undetectable fraction corrections for CCSNe in LIRGs based on our monitoring data.