This report presents the overview of the results of investigation of transport properties of warm dense matter in the conditions with strong coupling generated as a result of the shock or multiple shock compression of substance up to the megabar pressure range. We consider the results of measurements of the electrical conductivity in two different regions. The first one is the high temperature region, where the temperatures are of the order or much higher than the ionization potential I of the compressed substance. The region of “pressure ionization” where T ≪ I is the most interesting from the point of view of the specific plasma phase transitions. A few amounts of experimental data on shock compressed matter viscosity are discussed. For the estimations of shear viscosity of strongly coupled plasma experimental data on measurements of electrical conductivity of hydrogen, deuterium and rare gases under intense shock compression were used. It is shown that the ratio of shear viscosity coefficient to volume density of entropy of strongly coupled plasma is of the order of a lower bound, predicted by Kovtun et al. (2005) in frames of string theory methods.