This talk presents our high resolution adaptive moving mesh methods for hyperbolic conservation laws and its Applications in fluid dynamics. referring to the Arbitrary Lagrangian Eulerian (ALE) formulation, they can be classified into two classes, i.e. indirect method and direct method. The indirect ALE-type method is formed by two independent parts: PDE evolution and mesh-redistribution. The first part can be any appropriate high-resolution scheme, and the second part is based on an iterative procedure. In each iteration, meshes are first redistributed by an equidistribution principle, and then on the resulting new grids the underlying numerical solutions are updated by a conservative-interpolation formula. The iteration for the mesh redistribution at a given time step is complete when the meshes governed by a nonlinear equation reach the equilibrium state. The direct ALE-type method is built on the finite volume approximation of the PDE equation in curvilinear coordinates, the discrete geometric conservation laws, and the mesh adaptation implemented by iteratively solving the Euler-Lagrange equations of the mesh adaption functional in the computational domain with suitably chosen monitor functions. We also develop entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic equations. Several numerical results show that our ES adaptive moving mesh schemes effectively capture the localized structures, such as sharp transitions or discontinuities, and are more efficient than their counterparts on uniform mesh.