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Over the past decades, a tremendous amount of research has been done on the use of machine learning for speech processing applications, especially speech recognition. However, in the past few years, research has focused on utilizing deep learning for speech-related applications. This new area of machine learning has yielded far better results when compared to others in a variety of applications including speech, and thus became a very attractive area of research. This paper provides a thorough examination of the different studies that have been conducted since 2006, when deep learning first arose as a new area of machine learning, for speech applications. A thorough statistical analysis is provided in this review which was conducted by extracting specific information from 174 papers published between the years 2006 and 2018. The results provided in this paper shed light on the trends of research in this area as well as bring focus to new research topics.