Before designing a controller, one must be sure that the plant is controllable. Amplified controller signals must reach actuators and must reach the system’s states in order to impact on its dynamic behaviour so that performance requirements can be met. The chapter recalls criteria of Kalman, Hautus and Gilbert that enable to decide whether a system is completely state controllable and introduces the Gramian controllability matrix along with a specific input signal that transfers an initial system state to a target state. The chapter also briefly addresses the transformation of state-space model to Jordan canonical form and to controller canonical form (CCF), respectively.