Speech enhancement has substantial interest in the utilization of speaker identification, video-conference, speech transmission through communication channels, speech-based biometric system, mobile phones, hearing aids, microphones, voice conversion etc. Pattern mining methods have a vital step in the growth of speech enhancement schemes. To design a successful speech enhancement system consideration to the background noise processing is needed. A substantial number of methods from traditional techniques and machine learning have been utilized to process and remove the additive noise from a speech signal. With the advancement of machine learning and deep learning, classification of speech has become more significant. Methods of speech enhancement consist of different stages, such as feature extraction of the input speech signal, feature selection, feature selection followed by classification. Deep learning techniques are also an emerging field in the classification domain, which is discussed in this review. The intention of this paper is to provide a state-of-the-art summary and present approaches for using the widely used machine learning and deep learning methods to detect the challenges along with future research directions of speech enhancement systems. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.