  Non-linear parametric resonances occur frequently in nature. Here we
summarize how they can be studied by means of perturbative methods. We show in
particular how resonances can affect the motion of a test particle orbiting in
the vicinity of a compact object. These mathematical toy-models find
application in explaining the structure of the observed kHz Quasi-Periodic
Oscillations: we discuss which aspects of the reality naturally enter in the
theory, and which one still remain a puzzle.
