An important aspect in the study of quark gluon matter is represented by the computation of its transport coefficients. Indeed, they contain important information about thermodynamics and the phase diagram of QCD. Furthermore, they are used as input parameters in hydrodynamical simulations of heavy-ion collision experiments. The electric conductivity is a transport coefficient which parameterizes the charge transport phenomena. It is expected to play a central role in the dynamics of the Quark Gluon Plasma (QGP), since electric and magnetic fields are generated in heavy-ion collisions. The computation of this quantity can be done using the so-called Kubo formulas where spectral functions of electric current-current correlation functions and conductivity are directly related. The spectral functions can be extracted from the correlators on the lattice. The two quantities are related by an integral relation which has to be inverted to extract spectral functions. This inversion can be done by using smearing techniques to look for approximate solutions. We performed the study of the conductivity in two cases. On the one hand, we present the lattice QCD study of the electromagnetic conductivity dependence on baryon density. A first discussion can be found in \cite{Astrakhantsev:2021uii}. On the other hand, we studied the electromagnetic conductivity in presence of strong magnetic fields, namely $eB=4,9~GeV$. This gives an evidence of the CME.