Speaker individuality information is among the most critical elements within speech signals. By thoroughly and accurately modeling this information, it can be utilized in various intelligent speech applications, such as speaker recognition, speaker diarization, speech synthesis, and target speaker extraction. In this article, we aim to present, from a unique perspective, the developmental history, paradigm shifts, and application domains of speaker modeling technologies within the context of deep representation learning framework. This review is designed to provide a clear reference for researchers in the speaker modeling field, as well as for those who wish to apply speaker modeling techniques to specific downstream tasks.