The chapter presents the basic principles of fractional calculus and its application to the design and tuning of controllers for generic position and velocity systems. The complete tuning procedures for fractional-order PI/PD/PID controllers are presented, as well as some worked-out examples. The advantages of using fractional-order controllers over the traditional integer-order controllers are explained and validated using three examples, including an open-loop unstable system, a velocity, as well as a position system. Details regarding the tuning steps are presented and simulation examples to highlight the closed-loop dynamics. Robustness is also analysed considering significant gain variations.