The pressure, radiation, and ionization from the warm (UV emitting) and hot (X-ray emitting) gas has a significant impact on the cold, star-forming interstellar medium. In the RADFEEDBACK project we carried out a comprehensive 3D study of the turbulent, multi-phase ISM in different environments that includes, for the first time, a proper treatment of UV and X-ray emission from stellar (primary) sources and extended (secondary) sources like cooling shock fronts and evaporating clouds. We did this by means of massively parallel, high-resolution 3D simulations that capture the complex interplay of gravity, magnetic fields, feedback from massive stars (ionizing radiation, radiation pressure, stellar winds, supernovae), heating and cooling including X-rays and cosmic rays, and chemistry. We developed a novel, original and highly efficient method, TreeRay, to accurately treat the transfer of radiation from multiple point and extended sources in the 3D simulations. In particular, based on TreeRay, we developed new methods to treat radiation pressure on dust and gas as well as the radiative transfer of cooling radiation in the Optical, UV, and X-ray bands. Radiation and chemistry were coupled to achieve self-consistent heating, cooling, and ionization rates. This enabled us to determine the efficiency of stellar feedback in different environments and to investigate which feedback process is dominant. Here we found that early feedback from massive stars regulates the star formation efficiency in galaxies, while supernovae initiate galactic outflows which are taken to larger scale heights via the Cosmic Ray pressure gradient that is replenished by the acceleration of Cosmic Rays in supernovae. In particular, we found that UV radiation has a major impact on limiting the star formation efficiency in dense molecular clouds, while stellar winds become dynamically dominant when the massive star is embedded in a lower-density, warm environment. Radiation pressure dominates in high-density, cold environments such as typically prevailing in massive star forming cores and massive giant molecular clouds. Moreover, accurate synthetic observations covering the large dynamic range from X-rays down to radio emission were generated to set the results in the proper observational context. We were also able to show that our 3D simulations can recover a multitude of observed molecular cloud properties, such that the simulations appear to be quite realistic and are used in a number of follow-up collaborative projects, such as how to design a future space mission to observe the signatures of molecular hydrogen formation and dissociation.