In this paper, we review the basics of compressed sensing and introduce its application to optimal control, called the maximum hands-off control. First, we present the mathematical formulation of compressed sensing and show a heuristic approach to the problem using the ℓ1 norm with efficient numerical algorithms. Then, we introduce the maximum hands-off control, the sparsest control, or the L0 optimal control. We show mathematical properties of the maximum hands-off control, such as the equivalence between the L0 and L1 optimal controls, necessary conditions, and the existence. We also show the time discretization method to numerically compute the maximum hands-off control. Finally, we showcase some extensions of the maximum hands-off control.