We review the phenonomena which occur in multiphoton physics when the electric field of the applied laser radiation becomes comparable with the Coulomb field strength seen by an electron in the ground state of atomic hydrogen. This field is reached at an irradiance of approximately . The normal perturbative photon-by-photon based picture of the interaction of individual electrons with the field is replaced by a tunnelling picture in which, in a time of the order of, or less than one optical cycle, atomic wavepackets are generated which escape the confining Coulomb potential. These wavepackets are strongly influenced by the laser, `quiver' and may be accelerated back to the parent ion in a recollision process. Phase-coherent effects locked to the laser field become important: high harmonics are generated from these recollisions. We discuss the theory of such effects, and review progress in understanding how this quiver motion can be coherently controlled. We discuss ionization dynamics and review mechanisms by which atoms may be stabilized in very strong fields. Finally, we discuss relativistic effects which occur at very high-intensities.