The matrix converter is an array of controlled semiconductor switches that connects directly the three-phase source to the three-phase load. This converter has several attractive features that have been investigated in the last two decades. In the last few years, an increase in research work has been observed, bringing this topology closer to the industrial application. This paper presents the state-of-the-art view in the development of this converter, starting with a brief historical review. An important part of the paper is dedicated to a discussion of the most important modulation and control strategies developed recently. Special attention is given to present modern methods developed to solve the commutation problem. Some new arrays of power bidirectional switches integrated in a single module are also presented. Finally, this paper includes some practical issues related to the practical application of this technology, like overvoltage protection, use of filters and ride-through capability.