AdS3 Integrability, Tensionless Limits, and Deformations: A Review

Motivated by the recent advances in the understanding of integrability for $AdS_3$ backgrounds, we present a lightning review of this approach, with particular attention to the "tensionless" limits (with zero and one unit of NSNS flux), and to the many integrable deformations of the supergravity backgrounds. Our aim is to concisely but comprehensively take stock of the state of the art in the field, in a way accessible to non-experts, and to highlight outstanding challenges. Along the way we reference where the various derivation of these results, which we mostly omit, can be found in full detail.