Strongly correlated electron systems display some of the most exotic ground states in condensed matter. In this thesis high pressure is used to tune the degree of electron correlations in systems of current interest. Their electronic and structural properties were investigated at high pressure using x-ray spectroscopy and scattering as well as transport techniques in a diamond anvil cell. The interplay between short- and long-range structural order, one-dimensional charge ordering, and superconductivity was studied in La1.875Ba0.125CuO4. At ambient pressure, this material displays charge ordering at the onset of a low temperature structural phase transition, resulting in strong suppression of superconductivity. The electronic ordering is shown here to be tightly coupled to short-range, rather than long-range, structural order. It is argued that persistence of charge order on a very short length scale is responsible for the marginal enhancement of superconductivity under pressure, being evidence of competing electronic correlations. The lanthanides Gd and Tb display an atomic-like partially filled 4f level at ambient pressure. Here, extreme pressure was used in an attempt to delocalize these 4f states. Instability in Tb\u27s 4f8 level emerges through 4f-conduction band hybridization, triggering a Kondo effect in the Y(Tb) alloy. In contrast, the half-filled 4f7 level in Gd remains stable to at least 120 GPa. Tb appears to become a strongly correlated Kondo lattice at high pressure, the properties of which are of great interest. Alkali metals display unexpected properties at high pressure which are suggested to be due to enhanced electronic correlation of the once nearly-free conduction electrons. In this thesis, the mechanisms leading to the low symmetry phases observed at high pressure in K, Rb, and Cs were investigated. These phases are suggested to develop from the pressure-induced localization of the conduction band, which triggers a Peierls-like distortion. Furthermore, stripe-like charge ordering is theoretically observed in Cs at high pressure, in close resemblance to La1.875Ba0.125CuO4, including proximity of charge order to superconductivity