The physical mechanisms associated with ablation of matter by laser irradiation are quite different in different regions of parameter space. The important parameters are the laser wavelength; the laser flux versus time, position, and angle of incidence at the target; and the target properties as well as the properties of the laser-transport medium adjacent to the irradiated target surface. Important target properties include surface contour, laser reflectivity and absorption depth, thermal diffusively, vaporization energy, Gruneisen coefficient, spall strength, ionization energies and plasma opacity versus temperature and density. As the flux increases, the process becomes less dependent on most of these target properties. Depending on the values of these various parameters, at relatively low fluxes targets can be vaporized and these vapors can be transparent to the laser beam. If a transparent liquid or solid transport medium exists in front of the vaporized target material, then a complicated contained- vaporization process takes place and the work done on the target by the vapors can be several orders of magnitude larger than with a gas or vacuum transport medium; the degree of work enhancement can depend strongly on the vapor condensability and condensed matter thermal conductivity. For short-pulselength irradiations of semi-transparent targets with a low- acoustic-impedance-laser-transport medium adjacent to the target, ablation needs to be a vacuum in order for the beam to be able to propagate to the target. For targets in a vacuum exposed to fluxes of this order (and considerably higher) and for long pulselengths, most of the laser energy will be absorbed (before reaching the critical surface) by inverse bremsstrahlung in material blown off from the target; at higher fluxes, the beam will be stopped at the critical surface producing localized absorption along with much higher energy densities and non-thermal equilibrium behavior. When the combination of pulselength, beam diameter, flux and target material are such that the blowoff becomes opaque to the laser and also the blowoff can traverse many beam diameters during the pulselength, then a complicated radiation-hydrodynamic process is involved with strong feedback between blowoff hydrodynamic expansion, laser absorption, radiation transport, and target ablation by plasma reradiation. In this paper the various ablation processes and potential applications are reviewed from the threshold for ablation up to fluxes of about 1013 W/cm2, with emphasis on three particular processes; namely, front-surface spallation, two-dimensional blowoff, and contained vaporization.