In the last decade, the trend toward higher efficiency and higher torque density electrical machines (EMs) without permanent magnets (PMs) for the industrial sector has rapidly increased. This work discusses the latest research and industrial advancements in synchronous reluctance machines (SynRMs), being the emergent motor topology gaining wide acceptance by many industries. This article presents an extensive literature review covering the background and evolvement of SynRM, including the most recent developments. Nowadays, SynRM has found its niche in the EM market, and the reasons for that are highlighted in this work together with its advantages and disadvantages. The key journal publications in SynRM topics are discussed presenting the biggest challenges and the latest advancements with particular regards to the design methodology. This article aims to provide a thorough overview to the research community and industry about SynRM. There is a clear potential for SynRM to take over a significant portion of the EM market in the near future to meet efficiency standards in industrial applications without the use of rare-Earth PM technology.