Short review of Yasuda-Shimada theorem and related topics

In this paper, we will present the past and the present situation of a very controversial topic in Finsler geometry: the necessary and sufficient conditions for a Randers space to be of constant curvature. The research on this subject started more than a quarter of century ago, but its final act was played only two years ago. Moreover, the history of Yasuda-Shimada theorem and few words on the life of Professor Yasuda are added. Finally miscellaneous topics studied by the Japanese group of Finsler geometers are reviewed.