In this chapter, we focus on the area of text-independent speaker verification, with an emphasis on unconstrained telephone conversational speech. We begin by providing a general likelihood ratio detection task framework to describe the various components in modern text-independent speaker verification systems. We next describe the general hierarchy of speaker information conveyed in the speech signal and the issues involved in reliably exploiting these levels of information for practical speaker verification systems. We then describe specific implementations of state-of-the-art text-independent speaker verification systems utilizing low-level spectral information and high-level token sequence information with generative and discriminative modeling techniques. Finally, we provide a performance assessment of these systems using the National Institute of Standards and Technology (NIST) speaker recognition evaluation telephone corpora.