  In the course of evolution, proteins undergo important changes in their amino
acid sequences, while their three-dimensional folded structure and their
biological function remain remarkably conserved. Thanks to modern sequencing
techniques, sequence data accumulate at unprecedented pace. This provides large
sets of so-called homologous, i.e.~evolutionarily related protein sequences, to
which methods of inverse statistical physics can be applied. Using sequence
data as the basis for the inference of Boltzmann distributions from samples of
microscopic configurations or observables, it is possible to extract
information about evolutionary constraints and thus protein function and
structure. Here we give an overview over some biologically important questions,
and how statistical-mechanics inspired modeling approaches can help to answer
them. Finally, we discuss some open questions, which we expect to be addressed
over the next years.
