Timely and accurate infrastructure monitoring is essential for ensuring the safety, resilience, and functionality of critical assets such as bridges, roads, pipelines, and buildings. Remote sensing technologies offer scalable, non-invasive, and high-resolution data acquisition capabilities, making them highly suitable for large-scale infrastructure assessment. This article presents a systematic review of recent advancements in three key components of remote sensing-based infrastructure monitoring: Recognition, Reconstruction, and Registration (3R). Recognition involves the identification and classification of infrastructure elements through methods such as supervised classification, object detection, and segmentation. Reconstruction focuses on generating high-fidelity three-dimensional models and enhanced imagery using techniques like LiDAR-based modeling, super-resolution, and image restoration methods. Registration aligns multi-sensor and multi-temporal data into a common spatial reference frame using traditional and learning-based techniques, enabling accurate change detection and data fusion. This review explores the practical implementations of these techniques in various infrastructure monitoring scenarios, including road network analysis, bridge monitoring, and building assessments. Key challenges are also identified, such as data scarcity, high-resolution image complexity, segmentation boundary inaccuracies, and the need for efficient, automated processing pipelines. By synthesizing current methods and highlighting ongoing limitations, this review provides a comprehensive foundation for future research and development of intelligent, robust, and real-time infrastructure monitoring systems powered by remote sensing. © 2025 IEEE.