The perovskite structure has an incredible versatility that results in myriad compounds with varied and eccentric behaviors. Perovskite oxides have been extensively studied and used for over 60 years. In order to expand on our already thorough knowledge of these compounds, it is necessary to use modern and creative experimental techniques. High-pressure synthesis and high oxygen-gas pressure annealing techniques are used to synthesize oxygen stoichiometric RNiO₃ (R = lanthanide). The particularly rich phase diagram of this compound allows for the study of the crossover from localized to itinerant electronic behavior and from an enhanced Pauli to a Curie-Weiss law paramagnetism. Single crystals of RFeO₃ are grown in order to analyze the spin canting in these antiferromagnetic samples. The size of the rare earth-cation is used to tune the magnitude of octahedral-tilt distortions. This tuning allows distinguishing between the two possible drivers for spin canting and weak ferromagnetism in these compounds, the octahedral-tilt-dependent single-ion anisotropy and the octahedral-tilt-independent Dzyaloshinskii-Moriya interaction. Although it is a fluoride compound, KCuF₃ has been used as an analogue to transition-metal oxide perovskites such as LaMnO₃ because of the similarity of their orbital ordering. Through the use of high-temperature neutron diffraction, it is shown that the orbital ordering and Jahn-Teller distortion in this compound are not lifted at the predicted temperature. Another mechanism for orbital ordering is identified. La₂[subscript-x] Sr [subscript x] CuO₄ has long been of interest as the progenitor system of the highTc superconductors. Despite having an exceedingly well-studied phase diagram in the over-doped region of its superconducting dome, little is known about this system in the region x > 0.3 because of the difficulty of synthesizing fully oxygen-stoichiometric samples. With high-oxygen-gas-pressure annealing and high-pressure synthesis, the completion of the phase diagram up to x = 1.0 is attempted. Finally, like many iridates, post-Perovskite CaIrO₃ exhibits a very strong spinorbit coupling of its 5d electrons. Because its magnetism is very weak, traditional methods to measure the magnitude of its orbital moment and spin-orbit coupling, such as neutron powder diffraction, are not viable. In order to address this issue, direct measurement of the orbital moments was conducted by using x-ray absorption spectroscopy and x-ray magnetic circular dichroism techniques. / text