Modern engineered systems are increasingly complex, comprising interconnected components within hierarchical structures that interact dynamically under operational and environmental influences. As these systems degrade, performance and reliability decline, with failures potentially causing severe economic and safety impacts. Robust algorithms are therefore essential for monitoring wear and performance in such environments. Machine learning has driven advances in data-driven for Prognostics and Health Management (PHM) approaches, which detect anomalies, diagnose degradation and faults, and predict their evolution from condition monitoring data. However, these methods often struggle to capture nonlinear, evolving relationships and lack robustness under novel conditions. Many focus narrowly on temporal dynamics or static interdependencies, overlooking evolving inter-sensor relationships indicative of incipient faults. Without modeling exogenous influences, they suffer high false alarm rates, leading to alarm fatigue. Accurate degradation monitoring requires understanding how operational history drives progression and how accumulated damage affects performance. Most methods model only operational dynamics, inferring latent dynamics at a single timescale and missing the coupling of slow degradation with fast dynamics. This results in noisy degradation estimates, limiting subsequent prognostic accuracy. Furthermore, operational loads, which significantly affect degradation, are often impractical to measure directly. Virtual sensing can estimate these loads from condition monitoring data, but the diversity of sensors, with varied signal characteristics and sampling frequencies, complicates integration. Existing methods typically handle only a single sensor modality, struggle to fuse heterogeneous data, and generalize poorly to extreme or underrepresented conditions. To tackle these challenges, this thesis proposes a unified framework with three interconnected modules that capture interdependencies and dynamic behaviors across system levels. Designed for hierarchical, interconnected systems, the modules work independently or together for comprehensive monitoring and decision-making. By leveraging temporal and relational learning, the framework effectively models dynamic interactions, integrates heterogeneous data, and captures multiscale behaviors, enabling robust fault detection, reliable load estimation in underrepresented conditions, and accurate degradation inference. Specifically, the framework includes: (1) a module that dynamically captures evolving inter-sensor relationships using attention-based inference in temporal graph neural networks and incorporates operational context into node dynamics, enabling early and robust fault detection; (2) a module that fuses multirate data and models intra- and inter-modality interactions through a heterogeneous temporal graph with modality-specific, condition-aware encoders for reliable virtual load sensing; and (3) a module that disentangles long-range, slow-fast dynamics using a hierarchical differential model with monotonicity constraints, providing accurate degradation inference and supporting proactive control. The framework demonstrates effectiveness and robustness through extensive evaluations on both simulated and real-world systems for condition monitoring and degradation inference. Primarily developed for industrial systems, it has also shown potential in infrastructure health monitoring