This paper presents a survey of recent research on sparsity-driven synthetic aperture radar (SAR) imaging.In particular, it reviews (i) analysis and synthesis-based sparse signal representation formulations for SAR image formation together with the associated imaging results; (ii) sparsity-based methods for wide-angle SAR imaging and anisotropy characterization; (iii) sparsity-based methods for joint imaging and autofocusing from data with phase errors; (iv) techniques for exploiting sparsity for SAR imaging of scenes containing moving objects, and (v) recent work on compressed sensing-based analysis and design of SAR sensing missions.