The spectral subtraction method is a classical approach for enhancement of speech degraded by additive background noise. The basic principle of this method is to estimate the short-time spectral magnitude of speech by subtracting estimated noise spectrum from the noisy speech spectrum. This is also achieved by multiplying the noisy speech spectrum with a gain function and later combining it with the phase of the noisy speech. Besides reducing the background noise, this method introduces an annoying perceptible tonal characteristic in the enhanced speech and affects the human listening, known as remnant musical noise. Several variations and implementations of this method have been adopted in past decades to address the limitations of spectral subtraction method. These variations constitute a family of subtractive-type algorithms and operate in frequency domain. The objective of this paper is to provide an extensive overview of spectral subtractive-type algorithms for enhancement of noisy speech. After the review, this paper is concluded by mentioning a future direction of speech enhancement research from spectral subtraction perspective.