  A discussion on the electrical conductivity of the quark-gluon plasma as
determined by lattice QCD is given. After a reminder of basic definitions and
expectations, various methods for spectral reconstruction are reviewed,
including the use of Ans\"atze and sum rules, the Maximum Entropy and
Backus-Gilbert methods, and Tikhonov regularisation. A comprehensive overview
of lattice QCD results obtained so far is given, including a comparison of the
different lattice formulations. A noticeable consistency for the conductivities
obtained is seen, in spite of the differences in the lattice setups and
spectral reconstruction methods. It is found that in the case of quenched QCD
little temperature dependence of $\sigma/T$ is seen in the temperature range
investigated, while for QCD with dynamical quarks a reduction of $\sigma/T$ in
the vicinity of the thermal crossover is observed, compared to its value in the
QGP. Several open questions are posed at the end.
