  We review the long-term survival chances of young massive star clusters
(YMCs), hallmarks of intense starburst episodes often associated with violent
galaxy interactions. We address the key question as to whether at least some of
these YMCs can be considered proto-globular clusters (GCs), in which case these
would be expected to evolve into counterparts of the ubiquitous old GCs
believed to be among the oldest galactic building blocks. 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. We discuss in detail the promise of using
high-resolution spectroscopy to make progress towards this goal, as well as the
numerous pitfalls associated with this approach. We also discuss the latest
progress in worldwide efforts to better understand the evolution of entire
cluster systems, the disruption processes they are affected by, and whether we
can use recently gained insights to determine the nature of at least some of
the YMCs observed in extragalactic starbursts as proto-GCs. We 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.

Astrophysics