A concise review on analytical mechanics methods for fractional dynamics was presented. It mainly focused on the analytical mechanics representations of fractional dynamical systems, the analytical mechanics methods for constructing a fractional dynamical model and a family of fractional dynamical models, three types of fractional infinitesimal transformation for Lie group, the analytical mechanics methods for symmetry, symmetrical perturbation, conformal invariance, algebraic structure, Poisson integral, integral invariant, gradient representation, stability of fractional dynamical systems, and the analytical mechanics method of fractional differential equations. The applications of more than 10 kinds of fractional dynamics models in physics, mechanics, biology and nonlinear science were introduced. It also pointed out some problems should be studied further in the future.