Nucleosynthesis in Supernovae

We present the status and open problems of nucleosynthesis in supernova explosions of both types, responsible for the production of the intermediate mass, Fe-group and heavier elements (with the exception of the main s-process). Constraints from observations can be provided through individual supernovae (SNe) or their remnants (e.g. via spectra and gamma-rays of decaying unstable isotopes) and through surface abundances of stars which witness the composition of the interstellar gas at their formation. With a changing fraction of elements heavier than He in these stars (known as metallicity) the evolution of the nucleosynthesis in galaxies over time can be determined. A complementary way, related to gamma-rays from radioactive decays, is the observation of positrons released in $\beta^{+}$ -decays, as e.g. from $^{26}\mbox{Al}$ , $^{44}\mbox{Ti}$ , $^{56,57}\mbox{Ni}$ and possibly further isotopes of their decay chains (in competition with the production of $e^{+}e^{-}$ pairs in acceleration shocks from SN remnants, pulsars, magnetars or even of particle physics origin). We discuss (a) the role of the core-collapse supernova explosion mechanism for the composition of intermediate mass, Fe-group (and heavier?) ejecta, (b) the transition from neutron stars to black holes as the final result of the collapse of massive stars, and the relation of the latter to supernovae, faint supernovae, and gamma-ray bursts/hypernovae, (c) Type Ia supernovae and their nucleosynthesis (e.g. addressing the $^{55}\mbox{Mn}$ puzzle), plus (d) further constraints from galactic evolution, $\gamma$ -ray and positron observations. This is complemented by the role of rare magneto-rotational supernovae (related to magnetars) in comparison with the nucleosynthesis of compact binary mergers, especially with respect to forming the heaviest r-process elements in galactic evolution.