Towards integrability for AdS3/CFT2

We review the recent progress towards applying worldsheet integrability techniques to the $AdS_3/CFT_2$ correspondence to find its all-loop S matrix and Bethe-Yang equations. We study in full detail the massive sector of $AdS_3\times S^3\times T^4$ superstrings supported by pure Ramond-Ramond (RR) fluxes. The extension of this machinery to accommodate massless modes, to the $AdS_3\times S^3\times S^3\times S^1$ pure-RR background and to backgrounds supported by mixed background fluxes is also reviewed. While the results discussed here were found elsewhere, our presentation sometimes deviates from the one found in the original literature in an effort to be pedagogical and self-contained.