It is impossible to summarize all the important work on the subject in this review, but we find it instructive to list a chronogram of several relevant milestones taking us to 2014, in the context of GR. The following is a list – necessarily incomplete and necessarily biased – of works which, in our opinion, have been instrumental to shape the evolution of the field. A more complete set of references can be found in the rest of this review.
⋅ 1910 – The analysis of finite difference methods for PDEs is initiated with Richardson .
⋅ 1916 – Schwarzschild derives the first solution of Einstein’s equations, describing the gravitational field generated by a point mass. Most of the subtleties and implications of this solution will only be understood many years later [687*].
⋅ 1917 – de Sitter derives a solution of Einstein’s equations describing a universe with constant, positive curvature . His solution would later be generalized to the case .
⋅ 1928 – Courant, Friedrichs and Lewy use finite differences to establish existence and uniqueness results for elliptic boundary-value and eigenvalue problems, and for the initial-value problem for hyperbolic and parabolic PDEs .
⋅ 1931 – Chandrasekhar derives an upper limit for white dwarf masses, above which electron degeneracy pressure cannot sustain the star [193*]. The Chandrasekhar limit was subsequently extended to NSs by Oppenheimer and Volkoff [590*].
⋅ 1939 – Oppenheimer and Snyder present the first dynamical collapse solution within GR .
⋅ 1947 – Modern numerical analysis is considered by many to have begun with the influential work of John von Neumann and Herman Goldstine , which studies rounding error and includes a discussion of what one today calls scientific computing.
⋅ 1957 – Regge and Wheeler [641*] analyze a special class of gravitational perturbations of the Schwarzschild geometry. This effectively marks the birth of BH perturbation theory, even before the birth of the BH concept itself.
⋅ 1958 – Finkelstein understands that the surface of the Schwarzschild geometry is not a singularity but a horizon . The so-called “golden age of GR” begins: in a few years there would be enormous progress in the understanding of GR and of its solutions.
⋅ 1963 – Kerr [466*] discovers the mathematical solution of Einstein’s field equations describing rotating BHs. In the same year, Schmidt identifies the first quasar (quasi-stellar radio source) . Quasars are now believed to be supermassive BHs, described by the Kerr solution.
⋅ 1964 – Seymour Cray designs the CDC 6600, generally considered the first supercomputer. Speeds have increased by over one billion times since.
⋅ 1964 – Using suborbital rockets carrying Geiger counters new sources of cosmic X-rays are discovered. One of these X-ray sources, Cygnus X-1, confirmed in 1971 with the UHURU orbiting X-ray observatory, is soon accepted as the first plausible stellar-mass BH candidate (see, e.g., ). The UHURU orbiting X-ray observatory makes the first surveys of the X-ray sky discovering over 300 X-ray “stars”.
⋅ 1965 – Penrose and Hawking prove that collapse of ordinary matter leads, under generic conditions, to spacetime singularities (the so-called “singularity theorems”) [608*, 401]. A few years later, Penrose conjectures that these singularities, where quantum gravitational effects become important, are generically contained within BHs – The cosmic censorship conjecture [610*, 767*].
⋅ 1966 – May and White perform a full nonlinear numerical collapse simulation for some realistic equations of state .
⋅ 1967, 1971 – Israel, Carter and Hawking prove that any stationary, vacuum BH is described by the Kerr solution [453, 188*, 403, 406*]. This result motivates Wheeler’s statement that “a BH has no hair” .
⋅ 1968 – Veneziano proposes his dual resonance model, which will later be understood to be equivalent to an oscillating string . This date is considered the dawn of SMT.
⋅ 1969 – Penrose shows that the existence of an ergoregion allows to extract energy and angular momentum from a Kerr BH . The wave analogue of the Penrose process is subsequently shown to occur by Zeldovich, who proves that dissipative rotating bodies (such as Kerr BHs, for which the dissipation is provided by the horizon) amplify incident waves in a process now called superradiance [827*, 828*].
⋅ 1970 – Zerilli [829, 830*] extends the Regge–Wheeler analysis to general perturbations of a Schwarzschild BH. He shows that the problem can be reduced to the study of a pair of Schrödinger-like equations, and applies the formalism to the problem of gravitational radiation emitted by infalling test particles.
⋅ 1970 – Vishveshwara  studies numerically the scattering of GWs by BHs: at late times the waveform consists of damped sinusoids (now called ringdown waves, or quasi-normal modes).
⋅ 1971 – Davis et al. [250*] carry out the first quantitative calculation of gravitational radiation emission within BH perturbation theory, considering a particle falling radially into a Schwarzschild BH. Quasi-normal mode (QNM) ringing is excited when the particle crosses the maximum of the potential barrier of the Zerilli equation, located close to the unstable circular orbit for photons.
⋅ 1973 – Bardeen, Carter and Hawking derive the four laws of BH mechanics .
⋅ 1973 – Thorne provides a criterium for BH formation, the hoop conjecture [750*]; it predicts collapse to BHs in a variety of situations including very high-energy particle collisions, which were to become important in TeV-scale gravity scenarios.
⋅ 1974 – Hulse and Taylor find the first pulsar, i.e., a radiating neutron star (NS), in a binary star system . The continued study of this system over time has produced the first solid observational evidence, albeit indirect, for GWs. This, in turn, has further motivated the study of dynamical compact binaries and thus the development of NR and resulted in the 1993 Nobel Prize for Hulse and Taylor.
⋅ 1975 – Using quantum field theory in curved space, Hawking finds that BHs have a thermal emission . This result is one of the most important links between GR and quantum mechanics.
⋅ 1980 – Bowen & York develop the conformal imaging approach resulting in analytic solutions to the momentum constraints under the assumption of maximal slicing as well as conformal and asymptotic flatness [121*].
⋅ 1985 – Stark and Piran  extract GWs from a simulation of rotating collapse to a BH in NR.
⋅ 1986 – McClintock and Remillard  show that the X-ray nova A0620-00 contains a compact object of mass almost certainly larger than , paving the way for the identification of many more stellar-mass BH candidates.
⋅ 1987 – ’t Hooft [736*] argues that the scattering process of two point-like particles above the fundamental Planck scale is well described and calculable using classical gravity. This idea is behind the application of GR for modeling trans-Planckian particle collisions.
⋅ 1992 – The LIGO detector project is funded by the National Science Foundation. It reaches design sensitivity in 2005 . A few years later, in 2009, the Virgo detector also reaches its design sensitivity .
⋅ 1992 – Bona and Massó show that harmonic slicing has a singularity-avoidance property, setting the stage for the development of the “1+log” slicing .
⋅ 1992 – D’Eath and Payne [256*, 257*, 258*, 259*] develop a perturbative method to compute the gravitational radiation emitted in the head-on collision of two BHs at the speed of light. Their second order result will be in good agreement with later numerical simulations of high-energy collisions.
⋅ 1993 – Christodoulou and Klainerman show that Minkowski spacetime is nonlinearly stable .
⋅ 1993 – Gregory and Laflamme show that black strings, one of the simplest higher-dimensional solutions with horizons, are unstable against axisymmetric perturbations [367*]. The instability is similar to the Rayleigh–Plateau instability seen in fluids [167*, 162]; the end-state was unclear.
⋅ 1993 – Choptuik finds evidence of universality and scaling in gravitational collapse of a massless scalar field. “Small” initial data scatter, while “large” initial data collapse to BHs [212*]; first use of mesh refinement in NR.
⋅ 1995, 1998 – Through a conformal decomposition, split of the extrinsic curvature and use of additional variables, Baumgarte, Shapiro, Shibata and Nakamura [695*, 78*] recast the ADM equations as the so-called BSSN system, partly building on earlier work by Nakamura, Oohara and Kojima [569*].
⋅ 1997 – Cactus 1.0 is released in April 1997. Cactus  is a freely available environment for collaboratively developing parallel, scalable, high-performance multidimensional component-based simulations. Many NR codes are based on this framework. Recently, Cactus also became available in the form of the Einstein Toolkit [521, 300*].
⋅ 1997 – Maldacena [536*] formulates the AdS/CFT duality conjecture. Shortly afterward, the papers by Gubser, Klebanov, Polyakov [372*] and Witten [798*] establish a concrete quantitative recipe for the duality. The AdS/CFT era begins. In the same year, the correspondence is generalized to non-conformal theories in a variety of approaches (see  for a review). The terms “gauge/string duality”, “gauge/gravity duality” and “holography” appear (the latter had been previously introduced in the context of quantum gravity [737*, 734*]), referring to these generalized settings.
⋅ 1998 – The hierarchy problem in physics – the huge discrepancy between the electroweak and the Planck scale – is addressed in the so–called braneworld scenarios, in which we live on a four-dimensional subspace of a higher-dimensional spacetime, and the Planck scale can be lowered to the TeV [46*, 40*, 638*, 639*].
⋅ 1998 – The possibility of BH formation in braneworld scenarios is first discussed [45, 69*]. Later work suggests BH formation could occur at the LHC [279*, 353*] or in ultra-high energy cosmic ray collisions [315, 33, 304].
⋅ 1999 – Friedrich & Nagy  present the first well-posed formulation of the initial-boundary-value problem (IBVP) for the Einstein equations.
⋅ 2000 – Shibata and Uryū  perform the first general relativistic simulation of the merger of two NSs. More recent simulations , using a technique developed by Baiotti and Rezzolla that circumvents singularity excision , confirm that ringdown is excited when the merger leads to BH formation. In 2006, Shibata and Uryū perform NR simulations of BH-NS binaries .
⋅ 2001 – Horowitz and Maeda suggest that black strings do not fragment and that the end-state of the Gregory–Laflamme instability may be an inhomogeneous string , driving the development of the field. Non-uniform strings are constructed perturbatively by Gubser [371*] and numerically by Wiseman, who, however, shows that these cannot be the end-state of the Gregory–Laflamme instability [789*].
⋅ 2005 – Pretorius [629*] achieves the first long-term stable numerical evolution of a BH binary. Soon afterwards, other groups independently succeed in evolving merging BH binaries using different techniques [159*, 65*]. The waveforms indicate that ringdown contributes a substantial amount to the radiated energy.
⋅ 2007 – Boyle et al. [122*] achieve unprecedented accuracy and number of orbits in simulating a BH binary through inspiral and merger with a spectral code that later becomes known as “SpEC” and uses multi-domain decomposition [618*] and a dual coordinate frame [678*].
⋅ 2008 – The first simulations of high-energy collisions of two BHs are performed [719*]. These were later generalized to include spin and finite impact parameter collisions, yielding zoom-whirl behavior and the largest known luminosities [697*, 720*, 717*, 716*].
⋅ 2009 – Dias et al. show that rapidly spinning Myers–Perry BHs present zero-modes, signalling linear instability against axially symmetric perturbations [272*], as previously argued by Emparan and Myers [305*]. Linearly unstable modes were subsequently explored in Refs. [271*, 270*].
⋅ 2009 – Collisions of boson stars show that at large enough energies a BH forms, in agreement with the hoop conjecture [216*]. Subsequent investigations extend these results to fluid stars [288*, 647*].
⋅ 2010 – Building on previous work , Lehner and Pretorius study the nonlinear development of the Gregory–Laflamme instability in five dimensions, which shows hints of pinch-off and cosmic censorship violation [511*].
⋅ 2011 – Bizoń and Rostworowski extend Choptuik’s collapse simulations to asymptotically AdS spacetimes [108*], finding evidence that generic initial data collapse to BHs, thereby conjecturing a nonlinear instability of AdS.