  We discuss the string theory on AdS_3. In the first half of this talk, we
review the SL(2,R) and the SL(2,C)/SU(2) WZW models which describe the strings
on the Lorentzian and Euclidean AdS_3 without RR backgrounds, respectively. An
emphasis is put on the fundamental issues such as the unitarity, the modular
invariance and the closure of the OPE. In the second half, we discuss some
attempts at clarifying such problems. In particular, we discuss the modular
invariance of the SL(2,R) WZW model and the calculation of the correlation
functions of the SL(2,C)/SU(2) WZW model using the path-integral approach.
