In this chapter, a matrix converter for direct AC-AC power conversion will be described. The matrix converter transfers power bidirectionally and controls the power factor of an input stage but does not require any DC-link capacitor. Hence, the matrix converter has received attention as a circuit system that has the capability of providing AC output of variable voltage and frequency without DC conversion from a commercial three-phase AC source. It is used in industrial applications that require high reliability, miniaturization, and sinusoidal input and output currents as well as bidirectional power flow capabilities.