Maritime transportation occupies an important position in global economy. Proper maintenance of key equipment such as ships is crucial for achieving high operational efficiency. Recently, Predictive Maintenance (PdM) has gained much attention lately, which determines the predictive plan based on the actual status of equipment and is more intelligent than traditional corrective and preventive maintenance strategies. In this paper, we review data-driven methods for predicting the Remaining Useful Life (RUL) of maritime equipment, which is a key index for triggering maintenance events. Data-driven methods are of interests because it can build accurate prediction models directly from multisource industrial sensor data, without the need of complex physical models. We briefly review shallow machine learning and deep learning-based methods, as well as methods combines data-driven and traditional model-based techniques. Finally, we discuss the challenges and future directions.