  Atomic scale nanowires attract enormous interest in a wide range of fields.
On the one hand, due to their quasi-one-dimensional nature, they can act as a
experimental testbed for exotic physics: Peierls instability, charge density
waves, and Luttinger liquid behavior. On the other hand, due to their small
size, they are of interest for future device applications in the
micro-electronics industry, but also for applications regarding molecular
electronics. This versatile nature makes them interesting systems to produce
and study, but their size and growth conditions push both experimental
production and theoretical modeling to their limits. In this review, modeling
of atomic scale nanowires on semiconductor surfaces is discussed focusing on
the interplay between theory and experiment. The current state of modeling
efforts on Pt- and Au-induced nanowires on Ge(001) is presented, indicating
their similarities and differences. Recently discovered nanowire systems (Ir,
Co, Sr) on the Ge(001) surface are also touched upon. The importance of
scanning tunneling microscopy as a tool for direct comparison of theoretical
and experimental data is shown, as is the power of density functional theory as
an atomistic simulation approach. It becomes clear that complementary strengths
of theoretical and experimental investigations are required for successful
modeling of the atomistic nanowires, due to their complexity.
