Stars more massive than ~ 20 − 25 M⊙ form a black hole at the end of their evolution. Stars with non-rotating black holes are likely to collapse “quietly” ejecting a small amount of heavy elements (faint supernovae). In contrast, stars with rotating black holes are likely to give rise to very energetic supernovae (hypernovae). We present distinct nucleosynthesis features of these two types of “black-hole-forming” supernovae. Nucleosynthesis in hypernovae is characterized by larger abundance ratios (Zn, Co, V, Ti)/Fe and smaller (Mn, Cr)/Fe than normal supernovae, which can explain the observed trend of these ratios in extremely metal-poor stars. Nucleosynthesis in faint supernovae is characterized by a large amount of fall-back. We show that the abundance pattern of the recently discovered most Fe-poor star, HE0107-5240, and other extremely metal-poor carbon-rich stars are in good accord with those of black-hole-forming supernovae, but not pair-instability supernovae. This suggests that black-hole-forming supernovae made important contributions to the early Galactic (and cosmic) chemical evolution. Finally we discuss the nature of first (Pop III) Stars.