  The Hubble Space Telescope (HST) has been instrumental in the discovery of
large numbers of extragalactic young massive star clusters (YMCs), often
assumed to be proto-globular clusters (GCs). As a consequence, the field of YMC
formation and evolution is thriving, generating major breakthroughs as well as
controversies on annual (or shorter) time-scales. Here, I review the long-term
survival chances of YMCs, hallmarks of intense starburst episodes often
associated with violent galaxy interactions. In the absence of significant
external perturbations, the key factor determining a cluster's long-term
survival chances is the shape of its stellar initial mass function (IMF). It
is, however, not straightforward to assess the IMF shape in unresolved
extragalactic YMCs. I also discuss the latest progress in worldwide efforts to
better understand the evolution of entire cluster populations, predominantly
based on HST observations, and conclude that there is an increasing body of
evidence that GC formation appears to be continuing until today; their
long-term evolution crucially depends on their environmental conditions,
however.
