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 an 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 not only 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.