<p>Customer-phase identification (CPI) in low-voltage distribution networks (LVDNs) is a critical task for maintaining system reliability, optimizing load balancing, and enhancing outage management. Traditional methods, predominantly hardware-based, involve high-frequency signal injection and specialized measurement devices, which, while accurate, are costly, labor-intensive, and difficult to scale in large or hard-to-access networks. Recent advancements in data-driven approaches have introduced alternatives that leverage readily available data from advanced metering infrastructure (AMI), offering cost-effective and scalable solutions. This paper presents a comprehensive survey of data-driven CPI techniques, classifying them into voltage-based and power/energy-based methods. We systematically analyze each approach, comparing them based on implementation cost, computational requirements, accuracy, and limitations. Voltage-based methods show promise in unbalanced systems, while power-based approaches excel in handling incomplete datasets. Knowledge gaps are identified, particularly concerning synchronization challenges, the impact of distributed energy resources (DERs), and the need for standardized testing datasets. The paper also provides recommendations for future research, emphasizing hybrid techniques that integrate voltage- and power-based data with machine learning to enhance identification accuracy. By addressing current limitations and proposing paths for advancement, this survey aims to guide researchers and practitioners in developing efficient CPI solutions for modern, data-rich distribution networks.</p>