Nowadays, in order to resolve the reliability problem in an enlarging distributed system, Byzantine fault tolerant system has researched popularly for its ability of tolerating arbitrary faults. In this paper, the definitions of Byzantine system and the estimation methods of improving the performance of Byzantine system are introduced. After that, some unresolved problems and some future development trends will be indicated. Finally, after analyzing the status of studies, several conclusions are drawn: 1) The cost of running a Byzantine system is still much higher than non-Byzantine system. Plans to increase the performance and decrease the overhead are need to be explored in further study. 2) While detecting Byzantine faults and proactive recovery can keep Byzantine system from breaking down, they still have some drawbacks. How to eliminate the drawbacks should be studied. 3) Different applications require different aspect of optimization. How to make practical Byzantine systems are needed to be studied.