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This paper presents single-channel speech enhancement techniques in spectral domain. One of the most famous single channel speech enhancement techniques is the spectral subtraction method proposed by S.F. Boll in 1979. In this method, an estimated speech spectrum is obtained by simply subtracting a preestimated noise spectrum from an observed one. Hence, the spectral subtraction method is not concerned with speech spectral properties. It is well known that the spectral subtraction method produces an annoying artificial noise in the extracted speech signal. On the other hand, recent successful speech enhancement methods positively utilize the speech property and achieve an efficient speech enhancement capability. This paper presents a historical review about some speech estimation techniques and explicitly states the difference between their theoretical background. Moreover, to evaluate their speech enhancement capabilities, we perform computer simulations. The results show that an adaptive speech enhancement method based on MAP estimation gives the best noise reduction capability in comparison to other speech enhancement methods presented in this paper.