In this thesis results of x-ray scattering and neutron scattering experiments on several strongly correlated transition metal oxides are presented. The prototypical charge ordered cuprate La1.48Nd0.4Sr0.12CuO4 was investigated using polarised neutron scattering. The results show that several proposed schemes for the magnetic order in this class of materials may be ruled out, however the data are consistent with one-dimensional stripe-like magnetic order. X-ray diffraction was used to show that the charge order is insensitive to an applied magnetic field, but might be affected by the existence of superconductivity. The magnetic excitations were also studied, and at low energies a gap in the magnetic fluctuations was observed and there is tentative evidence that this is related to magnetic anisotropy. The spin state transition in LaCoO3 was investigated using neutron inelastic scattering, and excitations reminiscent of those observed in ferromagnets above their critical temperatures were observed. The debate surrounding the nature of the excited spin state, S=1 or S=2, could not be resolved, however. The nature of the spin excitations in La0.82Sr0.18CoO3 was investigated using polarised neutrons and it was found that at low energies the excitations take the form of spin-waves. At higher energies this mode becomes heavily damped, and several possible damping mechanisms for this are discussed. Finally, the multiferroic material DyMn2O5 was studied using x-ray resonant scattering. A complex, temperature dependent, magnetic structure was found using a Dy resonance, which reflects an underlying order of the Mn ions. The measurements were in agreement with a theory of multiferroics based on acentric spin-density waves
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