QED in plasmas at ultra high field intensities

Lasers can now deliver extreme focused intensities; very soon, these intensities can exceed 1024 W/cm2. In these conditions QED processes can be important. These include strong radiation reaction, pair production, and electromagnetic cascades, and can impact the plasma dynamics. Similar conditions are also present in astrophysical objects such as pulsars and magnetars in connection with ultra high magnetic fields. I will present the numerical advances that are opening the possibility to understand self-consistently these scenarios, and illustrations from both laboratory and astrophysical scenarios will be presented. I will also discuss the main open questions and challenges when the interplay between collective plasma processes and QED is important.