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Sleep is an essential feature of living beings. For neonates, it is vital for their mental and physical development. Sleep stage cycling is an important parameter to assess neonatal brain and physical development. Therefore, it is crucial to administer newborn's sleep in the neonatal intensive care unit (NICU). Currently, Polysomnography (PSG) is used as a gold standard method for classifying neonatal sleep patterns, but it is expensive and requires a lot of human involvement. Over the last two decades, multiple researchers are working on automatic sleep stage classification algorithms using electroencephalography (EEG), electrocardiography (ECG), and video. In this study, we present a comprehensive review of existing algorithms for neonatal sleep, their limitations and future recommendations. Additionally, a brief comparison of the extracted features, classification algorithms and evaluation parameters is reported …