The discovery of the formation of surfactant aggregates in dense gases by Gale et al. (1987a) has sparked significant research interest in the last few years. In particular, it was observed that the anionic surfactant Aerosol-OT formed transparent and thermodynamically stable solutions in various compressed-gas solvents near their critical point. These solutions could accommodate significant amounts of water. Also, polar solutes and even high molecular weight proteins could be solubilized. Light and neutron scattering studies showed that surfactant and water were organized in the form of spherical micelles. In subsequent studies, other surfactants yielded similar results, and a variety of different phase constellations was observed as known from conventional liquid mixtures. However, the viscosities and diffusion coefficients of compressed near- or supercritical fluids are several orders of magnitude different from those of comparable liquid solvents. Interestingly, the phase behavior of these compressible microemulsions was found to be highly pressure-dependent. Many research groups have since contributed to this new area of interest. In this work, we briefly review the results reported up to now concerning the phase behavior and the microstructure of these novel systems. Following an initial summary in the form of a table, we present and discuss the obtained results. Special emphasis is given on the experimental techniques and the theoretical explanations provided for the various phenomena that have been observed.