The received signals of array are coherent because of the reflection and refraction in the multipath propagation. The presence of coherent signals leads to the rank loss of signal covariance matrix, which results in the invalidity of conventional high-resolution direction of arrival(DOA) estimation methods. Therefore a variety of algorithms have been presented to solve this problem, which recover the rank of covariance matrix by utilizing the special property of steering vector. Recently, there has been a growing interest in deriving new algorithms that can reduce the loss of array aperture and increase the number of resolvable signals as well as the accuracy of DOA estimation. In this paper, the yield of coherent signals and their effect on DOA estimation are introduced, and the data models are established. Then, the coherent DOA estimation algorithms are presented class by class depending on their decorrelation approaches. Finally, the future research directions are prospected.