  We expose the current experimental and theoretical situation of the
interesting case of the production of phi 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 phi-meson production in hadron-nucleon collisions on the
spectra of secondary phi, and on the ratios of phi/pi(-) and phi/K(-)
production cross sections, as well the corresponding ones for phi-meson
production on nuclear targets, are considered. In particular, it is seen that
the production of phi-mesons on nuclear targets presents unusually small shadow
corrections for the inclusive density in the central rapidity region.
