We discuss the capabilities of continuum (continuous backbone) robot structures in the performance of under-actuated grasping. Continuum robots offer the potential of robust grasps over a wide variety of object classes, due to their ability to adapt their shape to interact with the environment via non-local continuum contact conditions. Furthermore, this capability can be achieved with simple, low degree of freedom hardware. However, there are practical issues which currently limit the application of continuum robots to grasping. We discuss these issues and illustrate via an experimental continuum grasping case study. <br><br> <i>This paper was presented at the IFToMM/ASME International Workshop on Underactuated Grasping (UG2010), 19 August 2010, Montréal, Canada.</i>