After the Big Bang, production of heavy elements in the early Universe takes place in the first stars and their supernova explosions. The nature of the first supernovae, however, has not been well understood. The signature of nucleosynthesis yields of the first supernovae can be seen in the elemental abundance patterns observed in extremely metal-poor stars. Interestingly, those abundance patterns show some peculiarities relative to the solar abundance pattern, which should provide important clues to understanding the nature of early generations of supernovae. We review the recent results of the nucleosynthesis yields of massive stars. We examine how those yields are affected by some hydrodynamical effects during the supernova explosions, namely, explosion energies from those of hypernovae to faint supernovae, mixing and fallback of processed materials, asphericity, etc. Those parameters in the supernova nucleosynthesis models are constrained from observational data of supernovae and metal-poor stars.