<p>Functional data captures the integrated, heterogeneous information generated across the full lifecycle of industrial manufacturing processes, equipment operations, and products. A profound analysis of these data is essential to evolve industrial intelligent systems into a more advanced state. This paper begins by clarifying the core concepts and prevalent forms of functional data, detailing its distinct strengths in handling continuous streaming data. It then systematically reviews the application of Functional Data Analysis (FDA) in pivotal industrial domains, including adaptive sampling, condition monitoring, fault diagnosis, degradation modeling, remaining useful life (RUL) prediction, and functional transfer learning. To address inherent industrial challenges—such as multi-source heterogeneity, phase variability, and stringent physical constraints—we propose a structured hierarchical framework. This framework traverses from the physical data and functional representation layers to the stages of feature extraction and task-oriented decision-making. Finally, by converging cutting‑edge technologies like physics‑informed neural networks, causal inference, and generative AI, the paper outlines promising research trajectories in areas such as tensor‑based dimensionality reduction and interpretable modeling. </p>