In the domain of speech recognition many methods have been proposed over time like Gaussian mixture models (GMM), GMM with universal background model (GMM-UBM framework), joint factor analysis, etc. i-Vector subspace modeling is one of the recent methods that has become the state of the art technique in this domain. This method largely provides the benefit of modeling both the intra-domain and inter-domain variabilities into the same low dimensional space. In this survey, we present a comprehensive collection of research work related to i-vectors since its inception. Some recent trends of using i-vectors in combination with other approaches are also discussed. The application of i-vectors in various fields of speech recognition, viz speaker, language, accent recognition, etc. is also presented. This paper should serve as a good starting point for anyone interested in working with i-vectors for speech processing in general. We then conclude the paper with a brief discussion on the future of i-vectors.