Hybrid organic/inorganic halide perovskites such as methylammonium lead iodide, (MA)PbI3, have recently burst on the solar cell scene with record efficiencies after only a few years of development. In this colloquium I will discuss some of the unique properties of these and related inorganic materials, such as CsSnI3 and their relation to their success in solar cell applications. I will show how the key feature of their electronic band structure results in a number of unusual properties. They are excellent hole conductors, they have an anomalous dependence of the band gap on temperature, strong optical absorption and their gap can be fine tuned with chemical substitutions. While their small band gap, which is optimal for solar cells, is determined by the covalent bonding of Sn to its nearest neighbors, the bonding between SnI6 octahedra and Cs has aspects typical of strongly ionic compounds, leading to a strong contribution of the lattice vibrations to the dielectric screening. I will discuss the consequences of this on solar cell related properties and the challenges it presents to theory. The perovskite structure exhibits various phase transitions, related to rotations of the octahedral building blocks which are related to unstable vibrational modes. I will discuss the role of these phase transitions on the long-term stability of the materials.