From the aspect of statistical mechanics we summarize the most important features of structural modeling based on the inverse theorem of liquid state theory. We focus on the Reverse Monte Carlo (RMC) method. Compared to previous techniques of diffraction data processing RMC provides new opportunities to model and understand the structures of random condensed matter. Conceived for practical needs its theoretical foundation was never systematically studied before. Since numerous author use RMC unscrupulously often reaching false or completely wrong conclusions, we carried out an investigation to explore the most important theoretical properties of the method. First, we show how restrictive the rigorous theoretical justification of the inverse theorem is. We present results of a representative calculation using the Born-Green-Yvon equation for the determination of the pair-potential of a simple liquid. We discuss the major characteristics of a correct RMC algorithm. As an alternative for complicated molecular systems we describe a dynamic version of the stochastic algorithm. We briefly review attempts to use iterative schemes for pair-potential determinations or refinements on the bases of measured pair structures.