The Roman Space Telescope will have the first advanced coronagraph in space, with deformable mirrors (DMs) for wavefront control (WFC), low-order wavefront sensing and maintenance, and a photon-counting detector. It is expected to be able to detect and characterize mature, giant exoplanets in reflected visible light. Over the past decade, the performance of the coronagraph in its flight environment has been simulated with increasingly detailed diffraction and structural/thermal finite-element modeling. With the instrument now being integrated in preparation for launch within the next few years, the present state of the end-to-end modeling, including the measured flight components such as DMs, is described. The coronagraphic modes, including characteristics most readily derived from modeling, are thoroughly described. The methods for diffraction propagation, WFC, and structural and thermal finite-element modeling are detailed. The techniques and procedures developed for the instrument will serve as a foundation for future coronagraphic missions, such as the Habitable Worlds Observatory.