Fractal Market Hypothesis (FMH) was originated in 1960s and formulated in 1990s. As one of the forward theories in mathematical finance, FMH has offered a new prospect and methodology for the nonlinear dynamical capital market. This paper tentatively analyzes the cross-development between EMH and FMH, as well as the application and tendency of FMH. We firstly clarificate that FMH is not a substitution or alternative but a complement to EMH, and reveal that the intrinsic unity is their essential relationship. Then we emphasize repeatedly that studies of domestic mostly remain at initial stage. There have been too many empirical analyses to demonstrate the fractal structure of market, but relatively too little work of what the microscopic causes are or how to conduct portfolio selection and risk management according to FMH. Our basic discussion is supposed to conclude the logicality between different theories and application prospects of FMH. We hope cautiously that our personal views could inspire some guidance for further research.