  Physics in curved spacetime describes a multitude of phenomena, ranging from
astrophysics to high energy physics. The last few years have witnessed further
progress on several fronts, including the accurate numerical evolution of the
gravitational field equations, which now allows highly nonlinear phenomena to
be tamed. Numerical relativity simulations, originally developed to understand
strong field astrophysical processes, could prove extremely useful to
understand high-energy physics processes like trans-Planckian scattering and
gauge-gravity dualities. We present a concise and comprehensive overview of the
state-of-the-art and important open problems in the field(s), along with
guidelines for the next years. This writeup is a summary of the "NR/HEP
Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011.
