This thesis is concerned with in-situ time-, temperature- and pressure-resolved synchrotron X-ray powder diffraction investigations of a variety of inorganic compounds with twodimensional layer structures and three-dimensional framework structures. In particular, phase stability, reaction kinetics, thermal expansion and compressibility at non-ambient conditions has been studied for 1) Phosphates with composition MIV(HPO4)2·nH2O (MIV = Ti, Zr); 2) Pyrophosphates and pyrovanadates with composition MIVX2O7 (MIV = Ti, Zr and X = P, V); 3) Molybdates with composition ZrMo2O8. The results are compiled in seven published papers and two manuscripts.Reaction kinetics for the hydrothermal synthesis of α-Ti(HPO4)2·H2O and intercalation of alkane diamines in α-Zr(HPO4)2·H2O was studied using time-resolved experiments. In the high-temperature transformation of γ-Ti(PO4)(H2PO4)·2H2O to TiP2O7 three intermediate phases, γ'-Ti(PO4)(H2PO4)·(2-x)H2O, β-Ti(PO4)(H2PO4) and Ti(PO4)(H2P2O7)0.5 were found to crystallise at 323, 373 and 748 K, respectively. A new tetragonal three-dimensional phosphate phase called τ-Zr(HPO4)2 was prepared, and subsequently its structure was determined and refined using the Rietveld method. In the high-temperature transformation from τ-Zr(HPO4)2 to cubic α-ZrP2O7 two new orthorhombic intermediate phases were found. The first intermediate phase, ρ-Zr(HPO4)2, forms at 598 K, and the second phase, β-ZrP2O7, at 688 K. Their respective structures were solved using direct methods and refined using the Rietveld method. In-situ high-pressure studies of τ-Zr(HPO4)2 revealed two new phases, tetragonal ν-Zr(HPO4)2 and orthorhombic ω-Zr(HPO4)2 that crystallise at 1.1 and 8.2 GPa. The structure of ν-Zr(HPO4)2 was solved and refined using the Rietveld method.The high-pressure properties of the pyrophosphates ZrP2O7 and TiP2O7, and the pyrovanadate ZrV2O7 were studied up to 40 GPa. Both pyrophosphates display smooth compression up to the highest pressures, while ZrV2O7 has a phase transformation at 1.38 GPa from cubic to pseudo-tetragonal β-ZrV2O7 and becomes X-ray amorphous at pressures above 4 GPa.In-situ high-pressure studies of trigonal α-ZrMo2O8 revealed the existence of two new phases, monoclinic δ-ZrMo2O8 and triclinic e-ZrMo2O8 that crystallises at 1.1 and 2.5 GPa, respectively. The structure of δ-ZrMo2O8 was solved by direct methods and refined using the Rietveld method.