This chapter presents the two main contemporary views of the Stokes phenomenon. In
the first view known as Stokes smoothing, it is claimed that rather than experiencing discontinuities
at specific rays in the complex plane, an asymptotic expansion, when magnified on a suitable scale,
is a rapidly smoothed function. Here we show that this fallacious conclusion has arisen because an
asymptotic expansion for the Stokes multiplier has been truncated, thereby giving the misleading
impression that it is equal to a term involving the error function when it is in fact only the leading
term of a complicated expression that needs to be regularised. Based on resurgence analysis, the
second view bears very little semblance to the original discovery made by Stokes. In this view
the Stokes lines become analytic curves that are determined by setting the real part of the action
in the one-dimensional Schr¨ odinger equation to zero due to a strange interpretation of maximal
dominance in a complete asymptotic expansion. Hence, the resulting asymptotic forms are no
longer uniform over specific sectors of the complex plane in marked contrast to the conventional
view of the Stokes phenomenon.
