Compressed Sensing (CS) is a recently developed tool for signal acquisition and compression in a single stage. In this thesis, we explore the nascent field of compressive sensing for images and video. The performance of different CS acquisition and reconstruction schemes for images are compared and analyzed. The quality of reconstruction corresponding to different measurement fractions is observed. Frame-by-frame mode and video block mode of CS for video are explored. Hybrid schemes that combine the ideas of CS and that of traditional video compression algorithms are studied. Specifically, two schemes, one having two layers of linear measurements at the encoder and two rounds of reconstruction at the decoder, and a second scheme using iterative reweighting along with morphological image processing at the decoder to reconstruct with better quality for lesser measurements are implemented.