  The rapid developments of computational quantum chemistry methods and
supercomputing facilities motivate the renewed interest in the analysis of the
muon/electron interactions in $\mu$SR experiments with \emph{ab initio}
approaches. Modern simulation methods seem to be able to provide the answers to
the frequently asked questions of many $\mu$SR experiments: where is the muon?
Is it a passive probe? What are the interaction parameters governing the
muon-sample interaction? In this review we describe some of the approaches used
to provide quantitative estimations of the aforementioned quantities and we
provide the reader with a short discussion on the current developments in this
field.
