High-entropy alloys (HEAs) have been around since 2004. The breakthroughs in this field led to several potential applications of these alloys as refractory, structural, functional, and biomedical materials. In this work, a short overview on the concept of high-entropy alloys is provided, as well as the theoretical design approach. The special focus of this review concerns one novel class of these alloys: biomedical high-entropy alloys. Here, a literature review on the potential high-entropy alloys for biomedical applications is presented. The characteristics that are required for these alloys to be used in biomedical-oriented applications, namely their mechanical and biocompatibility properties, are discussed and compared to commercially available Ti6Al4V. Different processing routes are also discussed.