Despite the rapid progress of several three-dimensional (3D) printing technologies, there exists a critical barrier in-term of processability of high performance materials. Polyether-ether-ketone (PEEK) is known for its higher mechanical properties, chemical stability, biological stability and biocompatibility suitable for certain biomedical applications. Examining a growing body of scientific literature on 3D printing of biomedical polymers indicates that most of the studies are conducted using biomedical polymers such as poly-carpolactone, poly lactic acid, poly-glycolic acid, polyethylene and polyurethanes. However, studies on 3D Printing of PEEK is sparse owing to the higher temperatures needed for melting, lacking of availability of suitable feedstock, concerns over poor adhesion between layers, and time consuming and uneconomical processing steps. Given the unique nature of PEEK class of polymers, this manuscript closely examines 3D printability of PEEK for a range of biomedical applications. This manuscript also presents ideas, feasible solutions and enabling scientific mechanisms to improve the 3D printability of PEEK. This article will help the research community to strengthen the conceptual knowledge and insights on the 3D printing of PEEK based medical devices and tools, and future possibilities.