In this chapter, we consider optimal control problems with a control from the space of regular Borel measures. The motivation is to obtain optimal controls with a “small” support. Such problems are often referred to as sparse control problems. In contrast to the state-constrained problems discussed in Chap. 13 , where a Borel measure (Lagrange multiplier) appears on the right-hand side of the adjoint equation, here, the control variable from the measure spaces enters the state equation. We discuss two settings: full control and observation as well as disjoint control and observation. For both types of problems, we provide regularity analysis and discuss the structural properties of the optimal control. For instance, we show that the control is given as a linear combination of finitely many Dirac measures under certain assumptions. Then, we develop a priori error analysis for both settings by exploiting different levels of regularity of the state and adjoint variables.