A scientific session of the Physical Sciences Division of the Russian Academy of Sciences and the Joint Physical Society of the Russian Federation was held in the Conference Hall of the P N Lebedev Physics Institute, Russian Academy of Sciences, on 28 February 2007. The following reports were presented at the session:
1. Fortov V E (Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow) “Intense shock waves and extreme states of matter”.
2. Kanel\’ G I (Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow) “Shock-wave effects in condensed media: metastable states, relaxation processes.”
The review being published is a combined, comprehensive, and supplemented version of the reports presented at this scientific session of the Physical Sciences Division of the Russian Academy of Sciences on 28 February 2007.

We review the latest results of investigations into polymorphous transformations, the deformation, and the fracture of solids in different structural states subjected to shock waves of submicrosecond duration. The problem of attaining the ideal strength of a condensed material is discussed. An anomalous rise in dynamic field stress as the in test temperature increases was discovered for high-purity metals. The effects of superheating in the crystal state and premelting under tension, as well as failure waves in shock-compressed glasses, were also discovered.