In the last ten years, sparsity-driven sensing and recovery techniques called compressed sensing (CS) has received much attention in signal processing community. So far, foundation of CS theory has been successfully established and the key principle of CS is being actively applied to various applications including machine learning, medical imaging, 5G wireless communications and network. It is expected that the CS will play an important role in implementing future digital devices as the expense for achieving super-resolution and high dimension for data processing is growing rapidly. In this seminar, we will review the basic theory behind the CS and discuss the key principles useful in applying the CS technique to real applications. We will go through various recovery algorithms and discuss their shortcomings that should be overcome by the researchers. Finally, we will introduce our recent research results along with its potential applications.