We expose the current experimental and theoretical situation of the interesting case of the production of φ mesons in up to very high energy collisions of hadrons on both nucleon and nuclear targets, and we present a quantitavely good theoretical description of the corresponding experimental data, based on the formalism of the well established Quark-Gluon String Model, that has proved to be valid for a wide energy range. All the available experimental data for φ-meson production in hadron-nucleon collisions on the spectra of secondary φ, and on the ratios of φ/π − and φ/K − production cross sections, as well the corresponding ones for φ-meson production on nuclear targets, are considered. In particular, it is seen that the production of φ-mesons on nuclear targets presents unusually small shadow corrections for the inclusive density in the central rapidity region.