  We show that two ostensibly different versions of the asymptotic resurgence
introduced by Guardo, Harbourne and Van Tuyl in 2013 are the same. We also show
that the resurgence and asymptotic resurgence attain their maximal values
simultaneously, if at all, which we apply to a conjecture of Grifo. For radical
ideals of points, we show that the resurgence and asymptotic resurgence attain
their minimal values simultaneously. In addition, we introduce an integral
closure version of the resurgence and relate it to the other versions of the
resurgence. In closing we provide various examples and raise some related
questions, and we finish with some remarks about computing the resurgence.
