We present a review of deep learning algorithms dedicated to the processing of speckle noise in coherent imaging. We focus on methods that specifically process de-noising of input images. Four main classes of applications are described in this review: optical coherence tomography, synthetic aperture radar imaging, digital holography amplitude imaging, and fringe pattern analysis. We then present deep learning approaches recently developed in our group that rely on the retraining of residual convolutional neural network structures to process decorrelation phase noise. The paper ends with the presentation of a new approach that uses an iterative scheme controlled by an input SNR estimator associated with a phase-shifting procedure.