In this review paper, we report the characteristics of the critical current density in FeAs based superconductors which is newly discovered by Hosono group of Tokyo Institute of Technology on 2008. Since the many specimens in present stage are not single crystals, there are two kinds of critical current density observed in the specimens which are so-called local and global critical current densities. Therefore, it is necessary to evaluate both kinds of critical current densities. The history effect in which the global critical current density shows different values in increasing and decreasing magnetic field is also observed when the specimens have the local and the global critical current densities. The wire which critical current is 180 A is successfully developed with using the knowledge of abovementioned characteristics of two kinds of critical current densities and the history effect.