Open Problems of Practice and Principle in Numerical Relativity

I will give an overview of the fundamentals of numerical relativity. The need for approximation schemes whose solutions converge to those of the underlying continuum system and how, alongside new hardware and software tools, this drives the subject is stressed. Criteria for declaring a problem solved are also touched upon. I go on to describe a few open problems in 3+1 spacetime dimensions in pure general relativity. These include the treatment of future null-infinity, large mass-ratio binary black hole spacetimes, stellar surfaces, near-critical vacuum spacetimes, plus the robust evolution of black holes and their interiors. The central perspective is that of a multidisciplinary subject which is mature but in no sense complete.