Supernova shock breakout is a bright UV or X-ray flash associated with t the birth of supernovae. In core-collapse supernova explosions, a strong blast wave forms in a collapsing massive star due to the gravitational collapse of the iron core and the shock propagates toward the surface of the star. When the shock front is at sufficiently deep layers, hot photons created in the post-shock region cannot escape into the interstellar space due to the optically thick stellar mantle. However, as the shock propagates in the stellar interior, the optical depth of the layers stratified on the shock front eventually decreases and finally the photons having confined in the shocked region can diffuse out through the stellar envelope toward the interstellar space. At the moment, the hot photons are emitted from the shocked region and are observed as a UV or X-ray flash. Detecting these "fresh" photons from newly-born core-collapse supernovae has been a big observational challenge because of the difficulty of observing transients fading very quickly. However, we have an increasing number of direct and indirect detections of supernova shock breakout thanks to sophisticated transient survey projects. We are tackling this problem by radiation-hydrodynamic simulations. Our recent two-dimensional radiation-hydrodynamic simulations suggest that the light curves of the shock breakou can provide us important information on the shock wave propagating in the stellar envelope and the progenitor star. In this talk, I review theoretical and observational studies on supernova shock breakout and introduce our recent results.