I this talk I will describe the computation of scattering amplitudes of winding strings in three-dimensional Anti-de Sitter (AdS3) spacetime, both at tree level and at one loop. At tree level, it will enable me to verify a previous conjecture about the form of the maximally winding violating amplitudes. Then, trying to extend the analysis to the next-to-maximally winding violating case at tree level will lead me to propose a prescription for computing string amplitudes in AdS3 at one loop. I will show how the results obtained with such prescription are consistent with the Liouville theory description of SL(2,C)/SU(2) Wess-Zumino-Witten genus-one correlation functions.