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In order to explore structure-properties relationship, structural, electronic, elastic, optical (linear and nonlinear), piezoelectric, and electro-optic properties of three cesium iodate CsIO 3 polymorphs (monoclinic; M, rhombohedric; R, cubic; C) have been computed, discussed and compared by means of density functional theory DFT using the Tran and Blaha modified Becke-Johnson potential TB-mBJ and the Generalized Gradient Approximation GGA implemented in WIEN2K code. Also, the Pseudo-Potential Plane Waves method PP-PW and Local Density Approximation LDA embedded in ABINIT code were used. Calculated structural parameters are in agreement with experimental values with both methods and we found that GGA grades are the closest. Band gaps of M and R systems are both direct (4.00 and 5.13 eV respectively) which apparently increases with increasing structural symmetry. The centrosymmetric cubic system C has no apparent band gap and adopt a metallic behaviour. Noncentrosymmetric M and R phases show interesting piezoelectric and nonlinear optical properties with several similarities in electronic characteristics principally related to the pseudo-rhombohedric structure of the monoclinic M-CsIO 3 system.