With the growing interest in electrification and as hybrid and pure electric powertrains are adopted in more applications, electrical machine design is facing challenges in terms of meeting very demanding performance metrics for example high specific power, harsh environments, etc. This provides clear motivation to explore the impact of advanced materials and manufacturing on the performance of electrical machines. This paper provides an overview of additive manufacturing (AM) approaches that can be used for constructing permanent magnet (PM) machines, with a specific focus on additivelymanufactured iron core, winding, insulation, PM as well as cooling systems. Since there has only been a few attempts so far to explore AM in electrical machines (especially when it comes to fully additivelymanufactured machines), the benefits and challenges of AM have not been comprehensively understood. In this regard, this paper offers a detailed comparison of multiple multi-material AM methods, showing not only the possibility of fully additively-manufactured PM machines but also the potential significant improvements in their mechanical, electromagnetic and thermal properties. The paper will provide a comprehensive discussion of opportunities and challenges of AM in the context of electrical machines.