  Contact and related phenomena, such as friction, wear or elastohydrodynamic
lubrication, remain as one of the most challenging problem classes in nonlinear
solid and structural mechanics. In the context of their computational treatment
with finite element methods (FEM) or isogeometric analysis (IGA), the inherent
non-smoothness of contact conditions, the design of robust discretization
approaches as well as the implementation of efficient solution schemes seem to
provide a never ending source of hard nuts to crack. This is particularly true
for the case of beam-to-solid interaction with its mixed-dimensional 1D-3D
contact models. Therefore, this contribution gives an overview of current steps
being taken, starting from state-of-the-art beam-to-beam (1D) and
solid-to-solid (3D) contact algorithms, towards a truly general 1D-3D
beam-to-solid contact formulation.
