## 1 Introduction
Despite the listed advantages, matrix converters output/input voltage ratio is lower than one, meaning the output voltages are always lower than the input voltages. This limitation is more relevant for variable speed electrical drives, as it will result in the limitation of the electrical machine's mechanical speed. This issue is further addressed in section five. However, in grid connected systems that make use of power transformers, this issue can be simply mitigated using a transformer with suitable turns ratio. Also, in some applications such as in photovoltaic (PV) systems where the preferential current path is from an energy source to the grid, the matrix converter actually behaves as a boost converter which can bring advantages that are further explored in section four. Throughout this work the use of matrix converters in the conversion of AC/DC (direct current) or DC/AC is referred hereafter as a current source rectifier (CSR) when the preferential power flow is from the grid to the load and as a current source inverter (CSI) when the preferential power flow is from an energy source to the grid. The numerous contributions and developments of AC/AC matrix converters have significantly increased the technology maturity to a point where in a near future matrix converters can find their way to a wide number of applications, including AC/DC and DC/AC conversion. This change of paradigm motivated this review with the purpose to show research work on matrix converters operating as AC/AC, as AC/DC, or DC/AC, with practical application in the development of new smart-grid assets, sustainable transportation, renewable energy increased grid penetration, and innovations in electrical drives. The literature review took into consideration scientific articles with preference, but not limited to Q1 journals and renowned conferences with the search being conducted through IEEE Xplore and Google Scholar. This paper is divided into 7 sections, each providing special emphasis on tackling challenges of matrix converters in relevant future industry applications of power converters:  
* The first section briefly introduces practical considerations on the design of matrix converter-based topologies with a special care given to the bidirectional switches commutation methods. * The second section focuses in \"Enabling technologies for smart and resilient grids\", presenting matrix converter applications towards a smarter, more efficient, versatile and sustainable grid. * The third section presents prominent applications of matrix converters in the connection of renewable energies to the grid, a crucial topic with the increasing demand for decarburization. * The fourth section highlights how matrix converter-based topologies tackle challenges in future variable speed electric drives, whose impact spreads across almost all industrial fields
* Electric mobility promises the electrification of most transportation vehicles, and the interface between the grid and electric vehicles is the topic of the fifth section highlighting the contributions of matrix converters. * The sixth section covers potential contributions of matrix converters to the pursuit of more sustainable transportation means detailing work developed on electric aircraft, marine and traction applications. * The final section introduces future challenges and research needs for matrix converters whose development is crucial for the penetration of the matrix converter in the aforementioned applications.