String Theory on $ADS_{3}: some open questions

String theory on curved backgrounds has received much attention on account of both its own interest, and in its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain unanswered, in particular in the very simple case of three-dimensional anti-de Sitter space. I will very briefly review these problems, discuss in some detail the important issue of constructing a consistent spectrum for a string propagating on AdS3 plus torsion background, and comment on potential solutions