Sparse modeling is a methodological framework and research field focused on representing data or signals as a linear combination of a small number of elements from a predefined or learned dictionary. This approach investigates the inherent structure of data that permits such parsimonious representations, typically involving optimization techniques to identify solutions with minimal non-zero coefficients. Its significance stems from its ability to facilitate efficient data compression, noise reduction, feature extraction, and the solution of inverse problems such as compressed sensing across various scientific and engineering disciplines.