The Effective Potential, the Renormalisation Group and Vacuum Stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.