Following pioneering works [1], the 3D hybrid perovskites CH3NH3PbX3 have recently been shown to drastically improve the efficiency of Dye Sensitized Solar Cells (DSSC) [2]. It is predicted to open “a new era and a new avenue of research and development for low-cost solar cells … likely to push the absolute power conversion efficiency toward that of CIGS (20%) and then toward and beyond that of crystalline silicon (25%)” [3]. We have theoretically investigated by DFT and k.p method the crystalline phases relevant for photovoltaic applications [4]. Our findings reveal the dramatic effect of spin orbit coupling (SOC) on their multiple band gaps, sizably smaller for tin than for lead based materials. Critical electronic states and optical absorption are thoroughly investigated. Multibandgaps and multivalleys phenomena are important to understand the optical and transport properties. Effective masses are also inferred. Excitonic effects are simulated. Besides inversion of band edge states, their physical properties show a close match to conventional semiconductors, leading to a new class of semiconductors different from the materials usually employed in DSSC.