Core-collapse supernovae are among the most energetic explosions in the universe marking the catastrophic end of massive stars. In spite of rigorous studies for several decades, we still do not understand the explosion mechanism completely. Since they are related to many astrophysical phenomena such as nucleosynthesis, gamma-ray bursts and acceleration of cosmic rays, understanding of their physics has been of wide interest to the astrophysical community. In this paper, we review recent progress in the study of core-collapse supernovae focusing on the explosion mechanism, supernova neutrinos and the gravitational waves. Regarding the explosion mechanism, we present a review paying particular attention to the roles of multidimensional aspects, such as convection, rotation and magnetic fields, on the neutrino heating mechanism. Next, we discuss supernova neutrino, which is a powerful tool to probe not only deep inside the supernovae but also the intrinsic properties of neutrinos. For this purpose, it is necessary to understand neutrino oscillation which has been established recently by many experiments. Gravitational astronomy is also now becoming a reality. We present an extensive review on the physical foundations and the emission mechanism of gravitational waves in detail and discuss the possibility of their detections.
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