  This article introduces, and reviews recent work using, a simple optimisation
technique for analysing the nonlinear stability of a state in a dynamical
system. The technique can be used to identify the most efficient way to disturb
a system such that it transits from one stable state to another. The key idea
is introduced within the framework of a finite-dimensional set of ordinary
differential equations (ODEs) and then illustrated for a very simple system of
2 ODEs which possesses bistability. Then the transition to turbulence problem
in fluid mechanics is used to show how the technique can be formulated for a
spatially-extended system described by a partial differential equation (the
well-known Navier-Stokes equation). Within that context, the optimisation
technique bridges the gap between (linear) optimal perturbation theory and the
(nonlinear) dynamical systems approach to fluid flows. The fact that the
technique has now been recently shown to work in this very high dimensional
setting augurs well for its utility in other physical systems.
