The results of decades of studies on the Phillips chromium (Cr)/silica polymerization catalyst are briefly summarized. The application of several characterization methods has allowed a detailed knowledge of the structure and reactivity of Cr centres to be obtained. In particular, many aspects of this apparently simple single-site catalyst, including the heterogeneity, the modification of the ligand sphere upon interaction with many molecules and the initiation mechanism of the ethylene polymerization reaction, have been clarified. It is shown that based on the acquired knowledge, it is now possible to proceed further towards the intelligent modification of the ligand sphere with the scope to increase the reaction rate and selectivity. It is also illustrated that, besides polymerization/oligomerization reactions, it is possible to extend the study of Cr II reactivity towards new reactions.