Speech is often the only available modality to recognize the identity of a person (over the telephone, the radio, in the dark,...). Automatic speaker recognition has been studied for several decades. In this chapter the state of the current text-independant speaker verification research is reviewed. Basic principles of speaker recognition are first summarized. The choice of the speech features and speaker models are mostly related to the individual characteristics (variability) of the speakers’ voices. Besides the speaker’s variability, we are faced with other factors, such as microphone or transmission channel variabilities, that degrade the performances of speaker verification algorithms. Some of these issues are illustrated on recent NIST–2005 and 2006 speaker recognition evaluation campaigns.