In the context of the possible existence of large extra dimensions, and also the context of the AdS-CFT correspondence, there has been much interest in black holes solutions in theories of gravity and matter that are exotic - they might live in spacetime dimension other than 4, or have exotic matter and boundary conditions. I will review the types of physics that are accessible by studying such exotic black holes, ranging from LHC phenomenology to potential applications to condensed matter physics (via the AdS-CFT correspondence). One common theme is that traditional analytic methods
to find solutions tend not to work when confronted with these more exotic solutions and instead we are increasingly forced to use numerical techniques. I will discuss a numerical approach to finding static and stationary solutions, and give some example applications. I will also show how dynamical numerical simulations in these exotic contexts are playing an increasingly important role.