Clinical sleep scoring involves a tedious visual review of overnight polysomnograms by a human expert, according to official standards. It could appear then a suitable task for modern artificial intelligence algorithms. Indeed, machine learning algorithms have been applied to sleep scoring for many years. As a result, several software products offer nowadays automated or semi-automated scoring services. However, the vast majority of the sleep physicians do not use them. Very recently, thanks to the increased computational power, deep learning has also been employed with promising results. Machine learning algorithms can undoubtedly reach a high accuracy in specific situations, but there are many difficulties in their introduction in the daily routine. In this review, the latest approaches that are applying deep learning for facilitating and accelerating sleep scoring are thoroughly analyzed and compared with the state of the art methods. Then the obstacles in introducing automated sleep scoring in the clinical practice are examined. Deep learning algorithm capabilities of learning from a highly heterogeneous dataset, in terms both of human data and of scorers, are very promising and should be further investigated.