Recent progress in a Josephson computer technology is reviewed. A Josephson computer is very attractive because Josephson digital circuits have the potential for realizing LSI circuits with extremely high performance in both circuit speed and power dissipation. Recently, various Josephson LSIs, such as processors and memories, have been made successfully with Nb or NbN junctions, particularly in Japan. These junctions exhibit high reliability for thermal cycling and long term storage, and have a good uniformity of the Josephson tunnelling current due to the tri-layer junction sandwich process. On the basis of such progress in Josephson IC technology, research, on Josephson computers in which Josephson memories are installed with a processor, is now under way.