Stuttering is a speech disorder during which the flow of speech is interrupted by involuntary pauses and repetition of sounds. Stuttering identification is an interesting interdisciplinary domain research problem which involves pathology, psychology, acoustics, and signal processing that makes it hard and complicated to detect. Recent developments in machine and deep learning have dramatically revolutionized speech domain, however minimal attention has been given to stuttering identification. This work fills the gap by trying to bring researchers together from interdisciplinary fields. In this paper, we review comprehensively acoustic features, statistical and deep learning based stuttering/disfluency classification methods. We also present several challenges and possible future directions.