Petawatt (PW) lasers are unique tools to study plasmas under extreme conditions. There are many applications for these plasmas that potentially have an impact on a wide range of scientific disciplines. A number of these are highlighted here in this review including: fast ignition of fusion targets; high brightness x-ray harmonic generation from oscillating plasma surfaces and the production of super-strong magnetic fields. This is a rich field of investigation, and space prevents a detailed discussion of some of these fascinating topics, including electron and ion acceleration processes that were highlighted at the London conference. Fortunately, they are presented elsewhere in other invited papers in this special issue.