The tremendous progress in technology which we have witnessed during the last 30 years has led to enormous improvements of observational accuracy in all disciplines of fundamental astronomy. Relativity has been becoming increasingly important for modeling and interpretation of high accuracy astronomical observations during at least these 30 years. It is clear that for current accuracy requirements astronomical problems have to be formulated within the framework of General Relativity Theory. Many high-precision astronomical techniques have already required the application of relativistic effects, which are several orders of magnitude larger than the technical accuracy of observations. In order to interpret the results of such observations, one has to construct involved relativistic models. Many current and planned observational projects can not achieve their goals if relativity is not taken into account properly. The future projects will require the introduction of higher-order relativistic effects. To make the relativistic models consistent with each other for different observational techniques, to formulate them in the simplest possible way for a given accuracy, and to formulate them in a language understandable for astronomers and engineers who have little knowledge of relativity are the challenges of a multidisciplinary research field called Applied Relativity.