Preface by the Editors

During the dawn of General Relativity (GR), the formidable mathematical complexity of Einstein's theory made clear that the use of approximation (analytical) methods was mandatory, in order to tackle many problems of physical interest. Einstein himself pioneered both post-Newtonian and linearized approximations to investigate planetary motion and gravitational waves. Beyond the scope of these methods, the extreme regime of gravity – strong field with strong dynamics – would remain completely unexplored, largely due to the absence of any (astro) physical hints of its relevance, in the real universe.