Parallel robots are governed by closed-loop kinematic constraints and strongly coupled nonlinear dynamics, which limit the transferability of purely analytical model-based fault diagnosis methods under varying operating conditions. To address this issue, in this paper, we present a sensor-oriented synthesis of data-driven fault diagnosis for parallel robots. In the proposed study, we span sensor integration, signal characteristics and selection, and feature representation derived from sensor signals, providing a structured, sensor-centered perspective on data-driven diagnostic approaches. By organizing existing methods from the viewpoint of sensing and signal interpretation, we clarify the role of sensor information in fault detection and diagnosis performance. In addition, key challenges, emerging trends, and potential solution directions for future research are discussed, aiming to support the development of more effective sensor-oriented fault diagnosis frameworks for parallel robotic systems.