This paper discusses advanced radiation transport methodologies developed by the Virginia Tech Transport Theory Group (VT 3 G) for real-time simulations. These methodologies can be referred to as Multi-stage Response-function particle Transport (MRT) methods in which the problem of interest is partitioned into several stages that each can be represented by a response function or set of coefficients. These stages are combined into a linear system of equations which are solved iteratively using the pre-calculated databases of response functions and/or coefficients. These databases are obtained by performing a set of "forward" and/or "adjoint" transport calculations for different conditions, e.g., material and geometry, by the appropriate Monte Carlo and deterministic code systems. This paper demonstrates the MRT method through two real-life problems including inspection of a spent nuclear fuel pool for safeguard applications and simulation of an active interrogation system for a cargo container for nonproliferation and security applications. It is demonstrated that the method provides the capability of performing realtime simulations while preserving the accuracy of highly time-consuming transport calculations.