The abundance patterns of extremely metal-poor (EMP) stars provide us with important information on nucleosynthesis in supernovae (SNe) formed in a Pop III or EMP environment, and thus on the nature of the first stars in the Universe. We review nucleosynthesis yields of various types of those SNe, focusing on core-collapse (black-hole-forming) SNe with various progenitor masses, explosion energies (including Hypernovae), and asphericity. We discuss the implications of the observed trends in the abundance ratios among iron-peak elements, and the large C/Fe ratio observed in certain EMP stars with particular attention to recently discovered hyper metal-poor (HMP) stars. We show that the abundance pattern of the HMP stars with [Fe/H] <−5 and other EMP 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.