  The physical processes at the interface of a low-temperature plasma and a
solid are extremely complex. They involve a huge number of elementary processes
in the plasma, in the solid as well as charge, momentum and energy transfer
across the interface. In the majority of plasma simulations these surface
processes are either neglected or treated via phenomenological parameters.
However, those parameters are known only in some cases, so such an approach is
very inaccurate and does not have predictive capability. Therefore,
improvements are highly needed. In this paper we briefly summarize relevant
theoretical methods from solid state and surface physics that are able to
contribute to an improved simulation of plasma-surface interaction in the near
future. Full \textit{ab initio} quantum simulations are feasible only for
extremely short times and/or small system sizes. A substantial simplification
is achieved when electronic quantum effects are not treated explicitly. Then
one arrives at semi-classical molecular dynamics (MD) simulations for the heavy
particles that have become the main workhorse in surface science simulations.
Using microscopically founded potentials and force fields as an input, these MD
simulations approach the quality of \textit{ab initio} simulations, in many
cases. However, despite their simplified nature, these simulations require a
time step that is of the order or below one femtosecond making it prohibitive
to reach experimentally relevant scales of minutes. To bridge this gap in
length and time scales without compromising the first principles character of
the simulations, many physical and computational strategies have been put
forward in surface science. This paper presents a brief overview on different
methods and their underlying physical ideas, and we compare their strengths and
weaknesses.
