Ionic fluids have recently become the focus of both much theoretical and experimental investigations, due to their importance to various physical and biological systems. The behavior of such fluids is largely controlled by the nature of the long-range Coulomb interactions among the various charged species. A considerable literature already exists on the phase behavior of such systems, the nature of their phase transitions, and the values of the critical exponents that characterize the behavior of the fluids near the phase transition point. However, in many physical and biological systems, in addition to the ionic fluid, ionic quenched disorder also exits whereby positively- and negatively-charged centers are distributed spatially throughout the system, either randomly or with correlations of some extent. Such a quenched disorder greatly influences the phase behavior of the ionic fluid in the system. In particular, the behavior of such systems is highly interesting in two dimensions, where the Coulomb interaction decays very slowly (logarithmically) with the distance. In addition, computer simulation of system is considerably more difficult than that of the same fluid in the bulk. Here, we report the results of the first Monte Carlo simulations of the phase behavior of ionic fluids in two dimensions in such disordered media. The structure of various phases as a function of fluid density, type and strength of the disordered medium, and the system's temperature is studied in details.