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

Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD