Spin, charge and orbital ordering in various crystalline compounds have been studied under extreme conditions. The main techniques used were synchrotron X-ray and neutron powder diffraction. High-pressure conditions were obtained by using a diamond anvil cell and the Paris-Edinburgh cell. Changes in the valence state of BiNiO3 perovskite under pressure have been investigated by a neutron powder diffraction study and bond valence sum (BVS) calculations. At ambient pressure, BiNiO3 has the unusual charge distribution Bi3+0.5Bi5+0.5Ni2+O3 with ordering of Bi3+ and Bi5+ charges on the A sites of a highly distorted perovskite structure. High pressure neutron diffraction measurements show that the pressure-induced melting of the charge disproportionated state leads to a simultaneous charge transfer from Ni to Bi, so that the high pressure phase is metallic Bi3+Ni3+O3. This exceptional charge transfer between A and B site cations coupled to electronic instabilities at both sites gives rise to a remarkable variety of ground states. Furthermore, Rietveld analysis of low temperature neutron powder diffraction data shows that the structure of BiNiO3 remains triclinic (space grp 1P) throughout the temperature range 5 to 300 K. BVS calculations confirm that the charge distribution is Bi3+0.5Bi5+0.5Ni2+O3 down to 5 K. The magnetic cell is identical to that of the triclinic superstructure and a G-type antiferromagnetic model gives a good fit to the magnetic intensities, with an ordered Ni2+ moment of 1.76(3) μB at 5 K. However, BiNiO3 is ferrimagnetic due to the inexact cancellation of opposing, inequivalent moments in the low symmetry cell. The effect of high pressure on the structural properties of (EDT-TTF-CONH2)6[Re6Se8(CN)6], a conducting, molecular, mixed-valence, π-conjugated radical, cation salt has been examined using synchrotron X-ray diffraction and a diamond anvil cell set-up. It has previously been shown that this compound undergoes a low temperature phase transition from a rhombohedral (space group 3R) to a triclinic (space group1P) structure at ~150 K. This transition is caused by a charge ordering. A LeBail profile fitting of powder diffraction data revealed a change in compressibility at 0.7 GPa indicative of a phase transition. This was confirmed by single crystal data which showed that the structure remains rhombohedral )3(R, up i to 0.4 GPa but is triclinic )1(P at 0.8, 1.2 and 1.8 GPa. Hence, high pressure, as well as low temperature, can drive the charge ordering in (EDT-TTF-CONH2)6 [Re6Se8(CN)6]. The transition pressure is between 0.5-0.7 GPa at 300 K. The crystal and magnetic structures of the orbitally ordered perovskite KCrF3 have been determined from neutron powder diffraction measurement at temperatures from 3.5 to 300 K. A phase transition from a tetragonal to a monoclinic structure occurs at 250 K but the orbital ordering is sustained. Long range antiferromagnetic order of the A-type occurs below TN = 46 K and the refined magnetic moment for the Cr2+ sites was found to be 4.39(7) μB.