First, there has similar electrodynamics in general relativity. Next, the electromagnetic general relativity may be obtained. By the same method of equivalence principle for the electromagnetic field, whose curvatures are different for different ratios of charge to mass. We discussed the four possible tests. Third, for long-range gravitational field and electromagnetic field we research various unifications. Fourth, we discuss the quantization of these unified theories. Finally, nonlinearity and the negative matter are discussed. We believe that these investigations are all a broad space for exploration, and some potential application values.