  The first mathematical problems of the global analysis of dynamical models
can be traced back to the engineering problem of the Watt governor design.
Engineering requirements and corresponding mathematical problems led to the
fundamental discoveries in the global stability theory. Boundaries of global
stability in the space of parameters are limited by the birth of oscillations.
The excitation of oscillations from unstable equilibria can be easily analysed,
while the revealing of oscillations not connected with equilibria is a
chalfilenging task being studied in the theory of hidden oscillations. In this
survey, a brief history of the first global stability criteria development and
corresponding counterexamples with hidden oscillations are discussed.
