In this paper, we present a comprehensive analysis of intelligent fault diagnosis techniques for parallel Delta machines, with a particular focus on challenges related to data scarcity and distribution shifts. The primary objective of this review is to provide a systematic analysis of data-driven learning paradigms for sensor-based fault diagnosis in parallel Delta robots under limited labeled data and changing operating conditions. Unlike previous reviews that mainly summarize machine learning algorithms, in this work, we emphasize how heterogeneous sensor signals, multi-sensor information fusion, and intelligent sensing concepts improve diagnostic reliability and predictive maintenance in smart manufacturing environments. The overall framework of intelligent fault diagnosis is first outlined. Different learning paradigms—namely, supervised learning, semi-supervised learning, few-shot learning, and transfer learning—are then evaluated, with emphasis on their applicability under limited annotation conditions, diverse fault detection requirements, and varying operational environments. Hybrid deep learning models and ensemble learning strategies are further examined, demonstrating their effectiveness in capturing complex spatiotemporal dependencies. The role of gradient-based optimization methods and automated hyperparameter tuning is also analyzed in enhancing model robustness and performance. In addition, performance metrics and evaluation methodologies for both classification and regression tasks are reviewed, providing a consistent basis for benchmarking diagnostic systems. Overall, in this review, we provide a sensor-oriented perspective on intelligent fault diagnosis by integrating heterogeneous sensor information, advanced learning paradigms, and intelligent sensing concepts, while identifying current limitations and future research directions toward reliable predictive maintenance in smart manufacturing.