Abstract Changes in the hydrostatic pressure may significantly affect the spin dynamics of magnetically active compounds. Hence, objects exhibiting spin transitions have attracted attention of researchers in different fields. Since these transitions are reversible and do not cause the chemical decomposition of the compounds, spin state conversions can be responsible for the functional activity of materials as data storage media, external stimulus sensors or actuators for certain solid-state processes. Moreover, multispin compounds can demonstrate specific structural dynamics that is not inherent in diamagnetic compounds, which is of independent interest. The review presents the analysis of recent data on the effect of hydrostatic pressure on the crystal structure and magnetic properties of metal complexes with organic diamagnetic and paramagnetic ligands, exhibiting spin transitions and valence tautomerism, organic paramagnets and single-molecule magnets. The bibliography includes 179 references.