The speech signal is complex and contains a tremendous quantity of diverse information. The first step of extracting this information is to define an efficient representation that can model as much information as possible and will facilitate the extraction process. The I-vector representation is a statistical data-driven approach for feature extraction, which provides an elegant framework for speech classification and identification in general. This representation became the state of the art in several speech processing tasks and has been recently integrated with deep learning methods. This talk will focus on presenting variety of applications of the I-vector representation for speech and audio tasks including speaker profiling, speaker diarization and speaker health analysis. We will also show the possibility of using this representation to model and visualize information present in deep neural network hidden layers.