Using the latest generation of adaptive optics imaging systems together with laser guide stars on 8m-class telescopes, we are finally revealing the previously-hidden population of supernovae in starburst galaxies. Finding these supernovae and measuring the amount of absorption due to dust is crucial to being able to accurately trace the star formation history of our Universe. Our images of the host galaxies are amongst the sharpest ever obtained from the ground, and reveal much about how and why these galaxies are forming massive stars (that become supernovae) at such a prodigious rate.