  We review old and recent results on a special limit of string theory on
AdS$_3\times M_7$ with pure NS-NS fluxes: the limit in which the string length
$\ell_s=\sqrt{\alpha'}$ equals the AdS$_3$ radius $R $. At this point of the
moduli space, the theory exhibits special properties, which we discuss. Special
attention is focused on features of correlation functions that are related to
the non-compactness of the boundary CFT target space, and on how these features
change when the point $k\equiv R^2/\alpha ' =1$ is approached. Also, we briefly
review recent proposals for exact realizations of AdS/CFT correspondence at
this special point. \[\] This is the transcript of the talk delivered by the
author at the 8$^{\text{th}}$ edition of the Quantum Gravity in the Southern
Cone conference, held in Patagonia, December 16$^{\text{th}}$ -
20$^{\text{th}}$, 2019.
