Tuning the electronic properties of transition‐metal and rare‐earth compounds by virtue of changes of the crystallographic lattice constants offers controlled access to new forms of order. The development of tungsten carbide (WC) and moissanite Bridgman cells conceived for studies of the electrical resistivity up to 10 GPa, as well as bespoke diamond anvil cells (DACs) developed for neutron depolarization studies up to 20 GPa is reviewed. For the DACs, the applied pressure changes as a function of temperature in quantitative agreement with the thermal expansion of the pressure cell. A setup is described that is based on focusing neutron guides for measurements of the depolarization of a neutron beam by samples in a DAC. The technical progress is illustrated in terms of three examples. Measurements of the resistivity and neutron depolarization provide evidence of ferromagnetic order in SrRuO3 up to 14 GPa close to a putative quantum phase transition. Combining hydrostatic, uniaxial, and quasi‐hydrostatic pressure, the emergence of incipient superconductivity in CrB2 is observed. The temperature dependence of the electrical resistivity in CeCuAl3 is consistent with emergent Kondo correlations and an enhanced coupling of magneto‐elastic excitations with the conduction electrons at low and intermediate temperatures, respectively.