This paper provides an overview of text-independent speaker verification systems, focusing on the training and test phases. It details the cepstral analysis, a common speech parameterization technique, and explains Gaussian mixture modeling (GMM), the primary speaker modeling method. The paper also discusses alternatives like neural networks and support vector machines (SVMs). Score normalization, crucial for handling real-world data, is explained, along with the evaluation of speaker verification systems using the detection error trade-off (DET) curve. Extensions such as speaker tracking and segmentation are covered, along with applications in various domains. The paper concludes by highlighting research trends in speaker verification and addressing forensic issues.This paper provides an overview of text-independent speaker verification systems, focusing on the training and test phases. It details the cepstral analysis, a common speech parameterization technique, and explains Gaussian mixture modeling (GMM), the primary speaker modeling method. The paper also discusses alternatives like neural networks and support vector machines (SVMs). Score normalization, crucial for handling real-world data, is explained, along with the evaluation of speaker verification systems using the detection error trade-off (DET) curve. Extensions such as speaker tracking and segmentation are covered, along with applications in various domains. The paper concludes by highlighting research trends in speaker verification and addressing forensic issues.