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This paper presents a review of multi-objective deep learning methods that have been introduced in the literature for speech denoising. After stating an overview of conventional, single objective deep learning, and hybrid or combined conventional and deep learning methods, a review of the mathematical framework of the multi-objective deep learning methods for speech denoising is provided. A representative method from each speech denoising category, whose codes are publicly available, is selected and a comparison is carried out by considering the same public domain dataset and four widely used objective metrics. The comparison results indicate the effectiveness of the multi-objective method compared with the other methods, in particular when the signal-to-noise ratio is low. Possible future improvements that can be achieved are also mentioned.