Sparse signals are commonly expected in remote sensing and Earth observation. Along with the significant development of the compressive sensing theory, exploitation of sparsity in remote sensing became a very relevant and active field. Breakthroughs are brought in different remote sensing problems covering synthetic aperture radar, multispectral and hyperspectral image analysis, and LiDAR. Tailored to this special session, this tutorial gives a review, to the best knowledge of the session chair, on recent advances in sparsity exploitation in remote sensing and Earth observation, regarding the theory, applications and future trends.