This paper presents first an overview of the well-known voltage and current dc-link converter topologies used to implement a three-phase PWM ac-ac converter system. Starting from the voltage source inverter and the current source rectifier, the basics of space vector modulation are summarized. Based on that, the topology of the indirect matrix converter (IMC) and its modulation are gradually developed from a voltage dc-link back-to-back converter by omitting the dc-link capacitor. In the next step, the topology of the conventional (direct) matrix converter (CMC) is introduced, and the relationship between the IMC and the CMCs is discussed in a figurative manner by investigating the switching states. Subsequently, three-phase ac-ac buck-type chopper circuits are considered as a special case of matrix converters (MCs), and a summary of extended MC topologies is provided, including three-level and hybrid MCs. Therewith, a common knowledge basis of the individual converter topologies is established.