The selection of the appropriate core magnetic material for an electrical machine is one of the main design decisions that will significantly influence the power density and efficiency of the machine. The selection of the material is function of the torque/speed requirements and structure of the machine itself. Recent research have investigated different material options for electrical machine design and the basis of this paper is to provide a review and comparison of the research outcomes. The review is presented under three sections, viz. application of soft magnetic alloys, soft magnetic composites and amorphous magnetic materials. Based on the research outcomes, the most suitable applications for these different material categories have been identified. Future research directions of electrical machine design that may benefit the efficiency and power density are identified and associated research challenges are highlighted. The core loss parameters of state-of-the-art material in literature are compared and discussed.