Advancements in clinical practice have led to the classification of sleep stages (SSC) establishing an essential step up for physicians when evaluating sleep patterns and diagnosing sleep disorders. The traditional method of classifying sleep stages heavily depends on manual efforts by sleep experts, making it a time-intensive and labor-demanding task. To address this issue, computer-aided diagnosis (CAD) has emerged as a promising tool to support sleep experts, streamlining assessment and decision-making processes. Recently, CAD has incorporated artificial intelligence, particularly machine learning (ML) and deep learning (DL) techniques, which have gained significant attention in sleep stage classification (SSC). DL, in particular, provides greater accuracy and cost-effectiveness, leading to notable advancements. This study systematically reviews research on SSC utilizing ML and DL methods (ML-DL-SSC). It explores key aspects of ML-SSC and DL-SSC, such as signal and data representation, data preprocessing, deep learning models, and performance evaluation. The paper addresses three core questions: (1) Which signals are suitable for ML-DL-SSC? (2) What are the different ways to represent these signals? (3) What are the effective ML and DL models? By answering these questions, this paper aims to provide a comprehensive overview of ML-DL-SSC. This review explores the latest ML and DL approaches for sleep scoring and the challenges in integrating automated scoring into clinical practice along with the ability to achieve accuracy higher or similar to manual scoring, highlighting the potential of deep learning to improve sleep disorder diagnosis by analyzing a combination of different signals like polysomnography (PSG) and other varieties of data.