  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.
