Recent and anticipated advances in experimental technologies promise to enable new physical regimes in intense laser physics.They are enabled by anticipated increases in the intensities of both isolated attosecond pulses and of focused lasers as well as by techniques for extending harmonic generation to the x-ray regime.Theory has a large role to play in both interpreting and guiding experiments that make use of these new capabilities. The implications for theory are manifold, as indicated by the following examples:

• Increases in realized attosecond pulse intensities herald the advent of nonlinear attosecond physics, with the focus of theory being to elucidate and control electronic processes on their natural time scales.
• Ultra-high-order harmonic generation using mid-infrared driving laser fields may lead to the generation of sub-10 attosecond or even zeptosecond pulses (1 zs = 10^-21 s). The theoretical description of strong field processes involving mid-infrared driving laser fields faces increased demands on computational resources owing to the large-scale motions electrons undergo in such fields.
• For intensities > 10¹⁸ W/cm² the ponderomotive (quiver) energies of electrons in a laser field become comparable to the electron rest mass, implying the necessity for a relativistic theoretical description based on the Dirac equation. Moreover, as intensities increase, nonlinear quantum electrodynamics processes such as nonlinear Compton scattering, electron-positron pair creation, etc., as well as radiation reaction effects become increasingly important.
• Attosecond pulses imply high frequencies (from the extreme ultraviolet to the x-ray regime) which will interact mainly with core electrons in atoms, molecules and solids, where relativistic effects dominate. Nonlinear optics, based on nonperturbative theories of the Dirac equation, has to be addressed. Relativistic nonlinear optics is a new area of research in laser science.
• High Z elements exposed to intense attosecond pulses will experience coupling of core electrons to the vacuum or negative energy "sea,” thus allowing one to probe the vacuum and its possible effect on atomic and molecular structure in intense laser fields. As one example, it is unclear how to describe Auger effects in the presence of intense attosecond pulses in the relativistic regime. Solving the Dirac equation for particles in multi-center (molecular) potentials is another new problem in superintense fields.
• Zeptosecond pulses, having energies from 1 keV to 1 MeV, may eventually open the study and control of nuclear phenomena with intense, short laser pulses. When laser intensities exceed 10²⁴ W/cm², the proton’s quiver motion in the laser field approaches the proton rest mass, thus opening new theoretical problems in nonlinear, nonperturbative, relativistic quantum mechanics.

This program on the future directions of intense laser physics is timely because of the wealth of anticipated new phenomena, as illustrated by the examples noted above. It will bring together theorists and experimentalists to focus on issues such as these at the new frontiers of laser science.