Among perovskite solar cells, fully inorganic perovskite solar cells can compete as a stable and efficient alternative to hybrid cousins, with the recent report of a 13.4% efficient CsPbI3 perovskite quantum dot solar cell. Using synchrotron X-ray powder diffraction (SXRD), the detailed experimental structures of the three perovskite-phases of CsPbI3 (gamma at 325K, beta at 510K and alpha at 645K) have been recently reported. Based on these experimental results, we investigate the electronic properties of all three phases using a recently developed symmetry-based tight-binding (TB) model [1] as well as DFT calculations including both spin-orbit coupling (SOC) and many-body (GW approximation) effects.In fact, TB models afford an atomic-scale description to computing various properties, including distorted structures, at a significantly reduced computational cost compared to first-principles approaches. It allows tackling more difficult issues in terms of size, with complex heterostructures, nanostructures or composite materials, as well as properties with a great diversity of physical phenomena.The original empirical sp3 tight-binding (TB) model has been built for the reference Pm3m cubic phase of halide perovskite structures of general formula ABX3 and the TB parameters have been calibrated using available experimental and theoretical data for MAPbI3 (MA=CH3NH3+) [1]. To investigate less symmetric structure, such as the beta and gamma phases of CsPbI3, we show that this model can be extended by means of a simple d-2 Harrisson law, which allows tackling bond length variation. Given that very few experimental results are available on these phases of CsPbI3, we used the initial parameterization performed on MAPbI3. In order to gauge the quality and performances of this TB model, we further performed DFT calculations including both self-consistent GW corrections and relativistic effects (SOC). The band structure obtained with our TB model agrees nicely with results obtained from first-principles calculations. The model is then further exploited to inspect effect related to anharmonicity and results support the hypothesis of dynamical Rashba effects in CsPbI3. We may expect that such a model will be as relevant to the future of perovskite device modeling, as it has proved efficient for conventional semiconductors.