A review is conducted to deeply analyse and map the research landscape of current technologies in finger vein (FV) biometric authentication in medical systems into a coherent taxonomy. This research focuses on articles related to the keywords 'biometrics', 'finger veins' and 'verification' and their variations in three major databases, namely, Web of Science, ScienceDirect and IEEE Xplore. The final set of collected articles related to FV biometric authentication systems is divided into software-and hardware-based systems. In the first category, software development attempts are described. The experiment results, frameworks, algorithms and methods that perform satisfactorily are presented. Moreover, the experiences obtained from conducting these studies are discussed. In the second category, hardware development attempts are described. The final articles are discussed from three aspects, namely, (1) number of publications, (2) problem type, proposed solutions, best results and evaluation methods in the included studies and (3) available databases containing different scientific work collected from volunteers, such as staff and students. The basic characteristics of this emerging field are identified from the following aspects: motivations of using FV biometric technology in authentication systems, open challenges that impede the technology's utility, authors' recommendations and future research prospects. A new solution is proposed to address several issues, such as leakage of biometrics that leads to serious risks due to the use of stolen FV templates and various spoofing and brute-force attacks in decentralised network architectures in medical systems, including access points and various database nodes without a central point. This work contributes to literature by providing a detailed review of feasible alternatives and research gaps, thereby enabling researchers and developers to develop FV biometric authentication medical systems further. Insights into the importance of such a technology and its integration into different medical applications and fields are also provided.