It is remarkable that large diversities of supernova properties such as brightness and explosion energy have been observed. It is challenging to explore the origin of unusual supernovae, e.g., extremely faint and extremely luminous supernovae, and the extremely energetic explosions (hypernovae) associated with the Gamma-Ray Bursts. In particular, we present a core-collapse hypernova model for extremely luminous type Ic SN 2007bi as an alternative to the pair-instability model. We discuss how nucleosynthetic properties resulted from unusual supernovae are connected with the unusual abundance patterns of extremely metal-poor stars. Such connections may provide important constraints on the properties of first stars.
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