Electricity theft is a major challenge for modern smart grids and Advanced Metering Infrastructure (AMI), as unauthorized consumption, meter tampering, abnormal load patterns, and fraudulent energy usage can cause significant technical and economic losses to power utilities. The large volume of data generated by smart meters provides an opportunity to identify abnormal electricity consumption patterns using advanced data-driven techniques. This review paper presents a comprehensive analysis of deep learning techniques used for smart meter electricity theft detection, with particular emphasis on LSTM, BiLSTM, GRU, hybrid deep learning, ensemble learning, and adaptive learning frameworks. The reviewed studies are analyzed with respect to detection accuracy, feature selection, data balancing, privacy preservation, false-positive reduction, synthetic theft generation, and the use of AMI-based electricity consumption data. The review also examines the role of benchmarking datasets and preprocessing techniques in improving the reliability of theft detection models. Furthermore, the study identifies major challenges including imbalanced theft data, evolving theft patterns, privacy concerns, false alarms, and generalization across different smart-grid environments. Overall, the review indicates that deep learning and hybrid intelligent techniques provide a promising foundation for developing reliable, adaptive, and scalable electricity theft detection systems for modern smart grids.