Recent theoretical and experimental research with short-pulse, high-intensity lasers is surveyed with particular emphasis on new physical processes that occur in interactions with low- and high-density plasmas. Basic models of femtosecond laser - solid interaction are described including collisional absorption, transport, hydrodynamics, fast electron and hard x-ray generation, together with recently predicted phenomena at extreme intensities, such as gigagauss magnetic fields and induced transparency. New developments in the complementary field of nonlinear propagation in ionized gases are reviewed, including field ionization, relativistic self-focusing, wakefield generation and scattering instabilities. Applications in the areas of x-ray generation for medical and biological imaging, new coherent light sources, nonlinear wave guiding and particle acceleration are also examined.