  The quest for the origin of matter in the Universe had been the subject of
philosophical and theological debates over the history of mankind, but
quantitative answers could be found only by the scientific achievements of the
last century. A first important step on this way was the development of
spectral analysis by Kirchhoff and Bunsen in the middle of the 19$^{\rm th}$
century, which provided first insight in the chemical composition of the sun
and the stars. The energy source of the stars and the related processes of
nucleosynthesis, however, could be revealed only with the discoveries of
nuclear physics. A final breakthrough came eventually with the compilation of
elemental and isotopic abundances in the solar system, which are reflecting the
various nucleosynthetic processes in detail.
  This review is focusing on the mass region above iron, where the formation of
the elements is dominated by neutron capture, mainly in the slow ($s$) and
rapid ($r$) processes. Following a brief historic account and a sketch of the
relevant astrophysical models, emphasis is put on the nuclear physics input,
where status and perspectives of experimental approaches are presented in some
detail, complemented by the indispensable role of theory.
