Compressive sensing (CS) studies the minimal utility of the data for accurate image reconstruction under the proper sensing scheme. Although the assumptions of CS theories are rarely strictly satisfied in medical imaging, CS has inspired numerous sparsity-based new imaging methodologies and algorithms to enable faster and better imaging for various applications. This tutorial starts with a brief overview of CS and its recent developments, and then introduces various sparsity transforms for static and dynamic images, followed by a few representative optimization algorithms for solving the formulated sparsity-based models, which cover several imaging applications in MRI, CT, and optical molecular imaging.