Leakage in water distribution systems is a significant problem worldwide, leading to wastage of water resources, compromised water quality and excess energy consumption. Leakage detection is essential to reduce the duration of leaks and data-driven methods are increasingly being used for this purpose. However, these models are data hungry and available observed data, especially leakage data, is limited in most cases. In addition, these data need to be manually processed to label whether leaks occur, which is time-consuming and costly. These are significant obstacles for the development and application of these methods. This article provides a comprehensive review of relevant journal papers, categorizing all data-driven methods into unsupervised anomaly detection, semi-supervised anomaly detection and supervised classification methods based on how the data are utilized for developing these methods. In addition, strategies to address data limitations are summarized from both data and model perspectives, including data creation, reduction of a model's data requirements and knowledge transfer. After detailing these strategies, research gaps are identified. Based on these, future research directions are suggested, highlighting the need for further research in data augmentation, development of semi-supervised classification methods, exploration of multi-classification methods with model updating mechanisms, and development of novel knowledge transfer methods.