Global Anti-deSitter space suffers from a nonlinear instability where small excitations of energy \(E\) form black holes on a timescale of \(t \sim 1/E\). However, some initial data appears to lie within an “island of stability”, where collapse does not occur within \(t \gg 1/E\). Furthermore, evidence for the instability has mostly been restricted to zero angular momenta. I will discuss some recent progress towards understanding these islands of stability, and in incorporating angular momenta.