This paper presents a general and comparative review of the advances of grid technologies in medical sciences since 2000, with a special emphasis on Europe and Japan. The EU has over the years funded several big projects in the Grid and now the cloud area, covering besides the high energy physics domain also bioinformatics and medical applications as in image analysis. Bioinformatics and pharmaceutical design have been the major targets of grid applications in Japan. Grids and clouds share many of the same goals and techniques, although clouds are more commercially oriented and privately provided services and grids are rather publicly initiated resource sharing platforms between institutions without strong economic objectives. In the future, merging these two may potentially solve inter-operation problems of grids, which have been limiting the propagation of biomedical grids.