In this thesis, we present ProxiSART, a flexible proximal framework for robust 3D cone beam tomographic reconstruction based on the Simultaneous Algebraic Reconstruction Technique (SART). We derive the proximal operator for the SART algorithm and use it for minimizing the data term in a proximal algorithm. We show the flexibility of the framework by plugging in different powerful regularizers, and show its robustness in achieving better reconstruction results in the presence of noise and using fewer projections. We compare our framework to state-of-the-art methods and existing popular software tomography reconstruction packages, on both synthetic and real datasets, and show superior reconstruction quality, especially from noisy data and a small number of projections.