Recent years have seen an increased interest in iridium oxides as correlated materials that combine Coulomb correlations and strong spin-orbit coupling, which drastically affects the electronic structure and ensuing magnetic properties. In this talk, I will present the structural characterization and magnetic behavior for two classes of iridates with the integer (4+) and fractional (4.5+) iridium valence, respectively.  The integer-valence A2IrO3 iridates (A = Li, Na) feature honeycomb or honeycomb-like arrays of the Ir4+ ions. Magnetic interactions between these ions are strongly anisotropic with different easy directions on different bonds, which leads to the so-called exchange (or Kitaev) frustration and non-trivial magnetic structures.1 After presenting the strategy of crystal growth for these compounds, I will describe their structural instabilities that become especially pronounced upon compression. Using x-ray diffraction under pressure, we disclose the dimerization transitions that shorten two out of six Ir-Ir distances on the hexagon and stretch the other four. I will then discuss the microscopic origin of this dimerization and its implications for magnetism.  The mixed-valence iridates with the overall composition Ba3MIr2O9 and 6H-type perovskite-related structures entail trivalent M ions, such as In3+ or Lu3+, as well as the Ir2O9 dimers built by two face-sharing IrO6 octahedra. The short Ir-Ir link leads to the strong orbital overlap, charge delocalization, and fractional valence of 4.5+. I will discuss two crystallographic aspects of these compounds, the symmetry-lowering transitions and anomalous thermal expansion. The transition from the hexagonal to monoclinic symmetry is observed around room temperature, e.g., at 270 K for Ba3InIr2O9. The symmetry lowers through octahedral rotations, similar to the conventional tilting distortions in cubic perovskites. Irrespective of these transitions, the intradimer Ir-Ir distance shows an anomalous thermal expansion at 500-600 K, which is reminiscent of the abrupt structural changes upon the low-spin to high-spin transformations in Co3+ oxides, and indeed accompanied by the changes in the local magnetic moment probed in high-temperature susceptibility measurements.