  Viscoelastic fluids are a common subclass of rheologically complex materials
that are encountered in diverse fields from biology to polymer processing.
Often the flows of viscoelastic fluids are unstable in situations where
ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the
elastic and viscous stresses. Perhaps more surprisingly, the instabilities
produce flows with the hallmarks of turbulence -- even though the effective
Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on
viscoelastic flow instabilities by integrating the input from speakers at a
recent international workshop: historical remarks, characterization of fluids
and flows, discussion of experimental and simulation tools, and modern
questions and puzzles that motivate further studies of this fascinating
subject. The materials here will be useful for researchers and educators alike,
especially as the subject continues to evolve in both fundamental understanding
and applications in engineering and the sciences.
