In recent decades, the matrix converter (MC) has emerged as a promising AC/AC converter that performs the direct AC-to-AC conversion. Because of its attractive features such as compact volume, bidirectional power flow, controllable input power factor and sinusoidal waveforms, there has been an increase in MC related research work. Many control techniques have been proposed to control MCs and many potential applications have been investigated. This paper presents the state-of-the-art review in the recent development of control strategies and applications of MCs, starting with MC fundamentals. Some relevant simulation and experimental results are presented to show the performance of the corresponding controllers in specific applications. A wide range of control techniques and potential application fields are covered. Industrial products and modules are also discussed. Comparisons of different control strategies and different applications are summarized and presented. It is concluded that the MC is a promising converter and more research and industry interest is expected, particularly in AC motor drives and renewable energy microgrids.