Current status of AdS instability

<!--HTML--><p>I will discuss the dynamics of asymptotically AdS spacetimes from General Relativity perspective. In particular I will present old [arXiv:1104.3702] and new [arXiv:1506.03519] evidence for the instability of AdS space (maximally symmetric solution of Einstein equations with negative cosmological constant) against gravitational collapse of arbitrarily small initial perturbations. The later was enabled by a powerful resonant approximation suggested in<br /> arXiv:1403.6471 and thoroughly developed in arXiv:1407.6273. On the other hand the negative cosmological constant allows for the existence of stable, time-periodic, asymptotically AdS solutions of Einstein equations [arXiv:1303.3186].</p>