The development of high performance and power dense electric machines invariably requires exploration of the design space to identify promising designs. Conventional electric machine design optimization techniques aim at identifying optimal values for parameterized geometric variables by varying them within a specified range using an optimization algorithm. However, such approaches are limited by the parameterization which is typically determined by manufacturing constraints and the experience of the designer. Optimizing electric machine performance by using the material distribution as a design handle is known as topology optimization. This approach is enabled by the recent advances in additively manufactured metals that allow manufacturing complex geometries. While the application of topology optimization to structural mechanics has been widely studied, its application to identify optimal electric machine designs is an emerging area of research. In this paper, the state-of-the-art in topology optimization of electric machines is reviewed. First, the need for topology optimization is described, and the benefits and challenges of this technique over the conventional parametric optimization are identified. Next, the different topology optimization techniques reported in literature are described and their relative merits are discussed. Finally, a research outlook is provided for this technology.