A theoretical approach to room acoustic simulations based on a radiative transfer model is developed by adapting the classical radiative transfer theory from optics to acoustics. The proposed acoustic radiative transfer model expands classical geometrical room acoustic modeling algorithms by incorporating a propagation medium that absorbs and scatters radiation, handling both diffuse and non-diffuse reflections on boundaries and objects in the room. The main scope of this model is to provide a proper foundation for a wide number of room acoustic simulation models, in order to establish and unify their principles. It is shown that this room acoustic modeling technique establishes the basis of two recently proposed algorithms, the acoustic diffusion equation and the room acoustic rendering equation. Both methods are derived in detail using an analytical approximation and a simplified integral equation of the proposed method, respectively, allowing a clear definition of the underlying assumptions, limitations, advantages and disadvantages.