Structured Compressed Sensing: From Theory to Applications Compressed sensing (CS) is an emerging field that has attracted significant research interest. Previous reviews focused on standard discrete-to-discrete measurement architectures using random matrices and standard sparsity models. Recent developments have expanded CS into new application areas, necessitating a reevaluation of CS fundamentals. Random matrices are being replaced by structured sensing architectures that align with feasible acquisition hardware. Standard sparsity models are being extended to include richer signal classes and broader data models, including continuous-time signals. The review highlights new directions and connections to traditional CS, aiming to serve both practitioners entering the field and researchers seeking to apply existing ideas in practical contexts. CS aims to bridge theory and practice by identifying the potential of structured CS strategies to transition from mathematical concepts to hardware implementation. CS has evolved beyond its initial focus on finite-dimensional sparse vectors, incorporating continuous-time signals and practical measurement schemes. Recent work in CS has been divided into two major areas: theory and applications related to non-random CS matrices with inherent structure, and signal representations beyond sparsity, including continuous-time signals with infinite-dimensional representations. The review discusses the importance of structured CS matrices, which can be derived from real-world applications such as wireless channels, analog sampling hardware, sensor networks, and optical imaging. The standard sparsity prior is being extended to include signals with low-dimensional structures and signals with arbitrary dimensions. The review also explores the use of structured CS matrices in analog sampling, leading to new hardware implementations for reduced-rate samplers based on extended CS principles. The review emphasizes the need for broader signal models and practical measurement schemes to accommodate the increasing demands of data acquisition and processing. The review concludes by highlighting the importance of structured CS in bridging theory and practice, enabling the development of practical applications for this emerging field.Structured Compressed Sensing: From Theory to Applications Compressed sensing (CS) is an emerging field that has attracted significant research interest. Previous reviews focused on standard discrete-to-discrete measurement architectures using random matrices and standard sparsity models. Recent developments have expanded CS into new application areas, necessitating a reevaluation of CS fundamentals. Random matrices are being replaced by structured sensing architectures that align with feasible acquisition hardware. Standard sparsity models are being extended to include richer signal classes and broader data models, including continuous-time signals. The review highlights new directions and connections to traditional CS, aiming to serve both practitioners entering the field and researchers seeking to apply existing ideas in practical contexts. CS aims to bridge theory and practice by identifying the potential of structured CS strategies to transition from mathematical concepts to hardware implementation. CS has evolved beyond its initial focus on finite-dimensional sparse vectors, incorporating continuous-time signals and practical measurement schemes. Recent work in CS has been divided into two major areas: theory and applications related to non-random CS matrices with inherent structure, and signal representations beyond sparsity, including continuous-time signals with infinite-dimensional representations. The review discusses the importance of structured CS matrices, which can be derived from real-world applications such as wireless channels, analog sampling hardware, sensor networks, and optical imaging. The standard sparsity prior is being extended to include signals with low-dimensional structures and signals with arbitrary dimensions. The review also explores the use of structured CS matrices in analog sampling, leading to new hardware implementations for reduced-rate samplers based on extended CS principles. The review emphasizes the need for broader signal models and practical measurement schemes to accommodate the increasing demands of data acquisition and processing. The review concludes by highlighting the importance of structured CS in bridging theory and practice, enabling the development of practical applications for this emerging field.